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Welcome to the Mathematical World!
Trigonometric Chocolate Bar!!!
What does it mean by Trigonometric Chocolate Bar!? Is it edible? Actually, this is a normal purpose trigonometric table, with the values prescribed on it in terms of radicals, equations or sets. The main specialty of this trigonometric "Chocolate Bar" is that it has two features, one is the value of each of the trigonometric values in terms of approximate decimals (click or tap on the values), and the other is the exact value in terms of radicals, equations or sets. Many of them are directly or indirectly derived from the basic trigonometric formulae of addition and subtraction. If there is any mistake, please contact us. Enjoy! Note that, \(\phi\) represents the golden ratio, which is equal to \(\frac{1+\sqrt{5}}{2}\), not that Empty Set or Alan Walker Set!!!.
| Angle (degrees) | Angle (radians) | \(\sin \theta\) | \(\cos \theta\) | \(\tan \theta\) | \(\cot \theta\) | \(\sec \theta\) | \(\csc \theta\) |
|---|---|---|---|---|---|---|---|
| \(0^\circ\) | \(0\) | \(0\) | \(1\) | \(0\) | \(\text{undefined}\) | \(1\) | \(\text{undefined}\) |
| \(1^\circ\) | \(\frac{\pi}{180}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n+1\right)!}\cdot\left(\frac{\pi}{180}\right)^{2n+1}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n\right)!}\cdot\left(\frac{\pi}{180}\right)^{2n}\) | \(\frac{\sin1^\circ}{\cos1^\circ}\) | \(\frac{\cos1^\circ}{\sin1^\circ}\) | \(\frac{1}{\cos1^\circ}\) | \(\frac{1}{\sin1^\circ}\) |
| \(2^\circ\) | \(\frac{\pi}{90}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n+1\right)!}\cdot\left(\frac{\pi}{90}\right)^{2n+1}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n\right)!}\cdot\left(\frac{\pi}{90}\right)^{2n}\) | \(\frac{\sin2^\circ}{\cos2^\circ}\) | \(\frac{\cos2^\circ}{\sin2^\circ}\) | \(\frac{1}{\cos2^\circ}\) | \(\frac{1}{\sin2^\circ}\) |
| \(3^\circ\) | \(\frac{\pi}{60}\) | \(\frac{\left(\phi-1\right)\left(\sqrt{6}+\sqrt{2}\right)-\left(\sqrt{6}-\sqrt{2}\right)\sqrt{4-\left(\phi-1\right)^{2}}}{8}\) | \(\frac{\left(\phi-1\right)\left(\sqrt{6}-\sqrt{2}\right)+\left(\sqrt{6}+\sqrt{2}\right)\sqrt{4-\left(\phi-1\right)^{2}}}{8}\) | \(\frac{\left(\phi-1\right)\left(\sqrt{6}+\sqrt{2}\right)-\left(\sqrt{6}-\sqrt{2}\right)\sqrt{4-\left(\phi-1\right)^{2}}}{\left(\phi-1\right)\left(\sqrt{6}-\sqrt{2}\right)+\left(\sqrt{6}+\sqrt{2}\right)\sqrt{4-\left(\phi-1\right)^{2}}}\) | \(\frac{\left(\phi-1\right)\left(\sqrt{6}-\sqrt{2}\right)+\left(\sqrt{6}+\sqrt{2}\right)\sqrt{4-\left(\phi-1\right)^{2}}}{\left(\phi-1\right)\left(\sqrt{6}+\sqrt{2}\right)-\left(\sqrt{6}-\sqrt{2}\right)\sqrt{4-\left(\phi-1\right)^{2}}}\) | \(\frac{8}{\left(\phi-1\right)\left(\sqrt{6}-\sqrt{2}\right)+\left(\sqrt{6}+\sqrt{2}\right)\sqrt{4-\left(\phi-1\right)^{2}}}\) | \(\frac{8}{\left(\phi-1\right)\left(\sqrt{6}+\sqrt{2}\right)-\left(\sqrt{6}-\sqrt{2}\right)\sqrt{4-\left(\phi-1\right)^{2}}}\) |
| \(4^\circ\) | \(\frac{\pi}{45}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n+1\right)!}\cdot\left(\frac{\pi}{45}\right)^{2n+1}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n\right)!}\cdot\left(\frac{\pi}{45}\right)^{2n}\) | \(\frac{\sin4^\circ}{\cos4^\circ}\) | \(\frac{\cos4^\circ}{\sin4^\circ}\) | \(\frac{1}{\cos4^\circ}\) | \(\frac{1}{\sin4^\circ}\) |
| \(5^\circ\) | \(\frac{\pi}{36}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n+1\right)!}\cdot\left(\frac{\pi}{36}\right)^{2n+1}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n\right)!}\cdot\left(\frac{\pi}{36}\right)^{2n}\) | \(\frac{\sin5^\circ}{\cos5^\circ}\) | \(\frac{\cos5^\circ}{\sin5^\circ}\) | \(\frac{1}{\cos5^\circ}\) | \(\frac{1}{\sin5^\circ}\) |
| \(6^\circ\) | \(\frac{\pi}{30}\) | \(\frac{\sqrt{12-3\phi^{2}}-\phi}{4}\) | \(\frac{\sqrt{3}\phi+\sqrt{4-\phi^{2}}}{4}\) | \(\frac{\sqrt{12-3\phi^{2}}-\phi}{\sqrt{3}\phi+\sqrt{4-\phi^{2}}}\) | \(\frac{\sqrt{3}\phi+\sqrt{4-\phi^{2}}}{\sqrt{12-3\phi^{2}}-\phi}\) | \(\frac{4}{\sqrt{3}\phi+\sqrt{4-\phi^{2}}}\) | \(\frac{4}{\sqrt{12-3\phi^{2}}-\phi}\) |
| \(7^\circ\) | \(\frac{7\pi}{180}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n+1\right)!}\cdot\left(\frac{7\pi}{180}\right)^{2n+1}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n\right)!}\cdot\left(\frac{7\pi}{180}\right)^{2n}\) | \(\frac{\sin7^\circ}{\cos7^\circ}\) | \(\frac{\cos7^\circ}{\sin7^\circ}\) | \(\frac{1}{\cos7^\circ}\) | \(\frac{1}{\sin7^\circ}\) |
| \(8^\circ\) | \(\frac{2\pi}{45}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n+1\right)!}\cdot\left(\frac{2\pi}{45}\right)^{2n+1}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n\right)!}\cdot\left(\frac{2\pi}{45}\right)^{2n}\) | \(\frac{\sin8^\circ}{\cos8^\circ}\) | \(\frac{\cos8^\circ}{\sin8^\circ}\) | \(\frac{1}{\cos8^\circ}\) | \(\frac{1}{\sin8^\circ}\) |
| \(9^\circ\) | \(\frac{\pi}{20}\) | \(\frac{\phi-\sqrt{4-\phi^{2}}}{2\sqrt{2}}\) | \(\frac{\sqrt{4-\phi^{2}}+\phi}{2\sqrt{2}}\) | \(\frac{\phi-\sqrt{4-\phi^{2}}}{\sqrt{4-\phi^{2}}+\phi}\) | \(\frac{\sqrt{4-\phi^{2}}+\phi}{\phi-\sqrt{4-\phi^{2}}}\) | \(\frac{2\sqrt{2}}{\sqrt{4-\phi^{2}}+\phi}\) | \(\frac{2\sqrt{2}}{\phi-\sqrt{4-\phi^{2}}}\) |
| \(10^\circ\) | \(\frac{\pi}{18}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n+1\right)!}\cdot\left(\frac{\pi}{18}\right)^{2n+1}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n\right)!}\cdot\left(\frac{\pi}{18}\right)^{2n}\) | \(\frac{\sin10^\circ}{\cos10^\circ}\) | \(\frac{\cos10^\circ}{\sin10^\circ}\) | \(\frac{1}{\cos10^\circ}\) | \(\frac{1}{\sin10^\circ}\) |
| \(11^\circ\) | \(\frac{11\pi}{180}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n+1\right)!}\cdot\left(\frac{11\pi}{180}\right)^{2n+1}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n\right)!}\cdot\left(\frac{11\pi}{180}\right)^{2n}\) | \(\frac{\sin11^\circ}{\cos11^\circ}\) | \(\frac{\cos11^\circ}{\sin11^\circ}\) | \(\frac{1}{\cos11^\circ}\) | \(\frac{1}{\sin11^\circ}\) |
| \(12^\circ\) | \(\frac{\pi}{15}\) | \(\frac{\sqrt{4-\left(\phi-1\right)^{2}}-\sqrt{3}\phi+\sqrt{3}}{4}\) | \(\frac{\phi-1+\sqrt{12-3\left(\phi-1\right)^{2}}}{4}\) | \(\frac{\sqrt{4-\left(\phi-1\right)^{2}}-\sqrt{3}\phi+\sqrt{3}}{\phi-1+\sqrt{12-3\left(\phi-1\right)^{2}}}\) | \(\frac{\phi-1+\sqrt{12-3\left(\phi-1\right)^{2}}}{\sqrt{4-\left(\phi-1\right)^{2}}-\sqrt{3}\phi+\sqrt{3}}\) | \(\frac{4}{\phi-1+\sqrt{12-3\left(\phi-1\right)^{2}}}\) | \(\frac{4}{\sqrt{4-\left(\phi-1\right)^{2}}-\sqrt{3}\phi+\sqrt{3}}\) |
| \(13^\circ\) | \(\frac{13\pi}{180}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n+1\right)!}\cdot\left(\frac{13\pi}{180}\right)^{2n+1}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n\right)!}\cdot\left(\frac{13\pi}{180}\right)^{2n}\) | \(\frac{\sin13^\circ}{\cos13^\circ}\) | \(\frac{\cos13^\circ}{\sin13^\circ}\) | \(\frac{1}{\cos13^\circ}\) | \(\frac{1}{\sin13^\circ}\) |
| \(14^\circ\) | \(\frac{7\pi}{90}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n+1\right)!}\cdot\left(\frac{7\pi}{90}\right)^{2n+1}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n\right)!}\cdot\left(\frac{7\pi}{90}\right)^{2n}\) | \(\frac{\sin14^\circ}{\cos14^\circ}\) | \(\frac{\cos14^\circ}{\sin14^\circ}\) | \(\frac{1}{\cos14^\circ}\) | \(\frac{1}{\sin14^\circ}\) |
| \(15^\circ\) | \(\frac{\pi}{12}\) | \(\frac{\sqrt{6}-\sqrt{2}}{4}\) | \(\frac{\sqrt{6}+\sqrt{2}}{4}\) | \(2-\sqrt{3}\) | \(2+\sqrt{3}\) | \(\sqrt{6}-\sqrt{2}\) | \(\sqrt{6}+\sqrt{2}\) |
| \(16^\circ\) | \(\frac{4\pi}{45}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n+1\right)!}\cdot\left(\frac{4\pi}{45}\right)^{2n+1}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n\right)!}\cdot\left(\frac{4\pi}{45}\right)^{2n}\) | \(\frac{\sin16^\circ}{\cos16^\circ}\) | \(\frac{\cos16^\circ}{\sin16^\circ}\) | \(\frac{1}{\cos16^\circ}\) | \(\frac{1}{\sin16^\circ}\) |
| \(17^\circ\) | \(\frac{17\pi}{180}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n+1\right)!}\cdot\left(\frac{17\pi}{180}\right)^{2n+1}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n\right)!}\cdot\left(\frac{17\pi}{180}\right)^{2n}\) | \(\frac{\sin17^\circ}{\cos17^\circ}\) | \(\frac{\cos17^\circ}{\sin17^\circ}\) | \(\frac{1}{\cos17^\circ}\) | \(\frac{1}{\sin17^\circ}\) |
| \(18^\circ\) | \(\frac{\pi}{10}\) | \(\frac{\phi-1}{2}\) | \(\frac{\sqrt{4-\left(\phi-1\right)^{2}}}{2}\) | \(\frac{\phi-1}{\sqrt{4-\left(\phi-1\right)^{2}}}\) | \(\frac{\sqrt{4-\left(\phi-1\right)^{2}}}{\phi-1}\) | \(\frac{2}{\sqrt{4-\left(\phi-1\right)^{2}}}\) | \(\frac{2}{\phi-1}\) |
| \(19^\circ\) | \(\frac{19\pi}{180}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n+1\right)!}\cdot\left(\frac{19\pi}{180}\right)^{2n+1}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n\right)!}\cdot\left(\frac{19\pi}{180}\right)^{2n}\) | \(\frac{\sin19^\circ}{\cos19^\circ}\) | \(\frac{\cos19^\circ}{\sin19^\circ}\) | \(\frac{1}{\cos19^\circ}\) | \(\frac{1}{\sin19^\circ}\) |
| \(20^\circ\) | \(\frac{\pi}{9}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n+1\right)!}\cdot\left(\frac{\pi}{9}\right)^{2n+1}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n\right)!}\cdot\left(\frac{\pi}{9}\right)^{2n}\) | \(\frac{\sin20^\circ}{\cos20^\circ}\) | \(\frac{\cos20^\circ}{\sin20^\circ}\) | \(\frac{1}{\cos20^\circ}\) | \(\frac{1}{\sin20^\circ}\) |
| \(21^\circ\) | \(\frac{7\pi}{60}\) | \(\frac{\left(\sqrt{6}+\sqrt{2}\right)\sqrt{4-\phi^{2}}-\phi\left(\sqrt{6}-\sqrt{2}\right)}{8}\) | \(\frac{\left(\sqrt{6}-\sqrt{2}\right)\sqrt{4-\phi^{2}}+\phi\left(\sqrt{6}+\sqrt{2}\right)}{8}\) | \(\frac{\left(\sqrt{6}+\sqrt{2}\right)\sqrt{4-\phi^{2}}-\phi\left(\sqrt{6}-\sqrt{2}\right)}{\left(\sqrt{6}-\sqrt{2}\right)\sqrt{4-\phi^{2}}+\phi\left(\sqrt{6}+\sqrt{2}\right)}\) | \(\frac{\left(\sqrt{6}-\sqrt{2}\right)\sqrt{4-\phi^{2}}+\phi\left(\sqrt{6}+\sqrt{2}\right)}{\left(\sqrt{6}+\sqrt{2}\right)\sqrt{4-\phi^{2}}-\phi\left(\sqrt{6}-\sqrt{2}\right)}\) | \(\frac{8}{\left(\sqrt{6}-\sqrt{2}\right)\sqrt{4-\phi^{2}}+\phi\left(\sqrt{6}+\sqrt{2}\right)}\) | \(\frac{8}{\left(\sqrt{6}+\sqrt{2}\right)\sqrt{4-\phi^{2}}-\phi\left(\sqrt{6}-\sqrt{2}\right)}\) |
| \(22^\circ\) | \(\frac{11\pi}{90}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n+1\right)!}\cdot\left(\frac{11\pi}{90}\right)^{2n+1}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n\right)!}\cdot\left(\frac{11\pi}{90}\right)^{2n}\) | \(\frac{\sin22^\circ}{\cos22^\circ}\) | \(\frac{\cos22^\circ}{\sin22^\circ}\) | \(\frac{1}{\cos22^\circ}\) | \(\frac{1}{\sin22^\circ}\) |
| \(23^\circ\) | \(\frac{23\pi}{180}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n+1\right)!}\cdot\left(\frac{23\pi}{180}\right)^{2n+1}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n\right)!}\cdot\left(\frac{23\pi}{180}\right)^{2n}\) | \(\frac{\sin23^\circ}{\cos23^\circ}\) | \(\frac{\cos23^\circ}{\sin23^\circ}\) | \(\frac{1}{\cos23^\circ}\) | \(\frac{1}{\sin23^\circ}\) |
| \(24^\circ\) | \(\frac{2\pi}{15}\) | \(\frac{\sqrt{3}\phi-\sqrt{4-\phi^{2}}}{4}\) | \(\frac{\phi+\sqrt{12-3\phi^{2}}}{4}\) | \(\frac{\sqrt{3}\phi-\sqrt{4-\phi^{2}}}{\phi+\sqrt{12-3\phi^{2}}}\) | \(\frac{\phi+\sqrt{12-3\phi^{2}}}{\sqrt{3}\phi-\sqrt{4-\phi^{2}}}\) | \(\frac{4}{\phi+\sqrt{12-3\phi^{2}}}\) | \(\frac{4}{\sqrt{3}\phi-\sqrt{4-\phi^{2}}}\) |
| \(25^\circ\) | \(\frac{5\pi}{36}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n+1\right)!}\cdot\left(\frac{5\pi}{36}\right)^{2n+1}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n\right)!}\cdot\left(\frac{5\pi}{36}\right)^{2n}\) | \(\frac{\sin25^\circ}{\cos25^\circ}\) | \(\frac{\cos25^\circ}{\sin25^\circ}\) | \(\frac{1}{\cos25^\circ}\) | \(\frac{1}{\sin25^\circ}\) |
| \(26^\circ\) | \(\frac{13\pi}{90}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n+1\right)!}\cdot\left(\frac{13\pi}{90}\right)^{2n+1}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n\right)!}\cdot\left(\frac{13\pi}{90}\right)^{2n}\) | \(\frac{\sin26^\circ}{\cos26^\circ}\) | \(\frac{\cos26^\circ}{\sin26^\circ}\) | \(\frac{1}{\cos26^\circ}\) | \(\frac{1}{\sin26^\circ}\) |
| \(27^\circ\) | \(\frac{3\pi}{20}\) | \(\frac{\sqrt{4-\left(\phi-1\right)^{2}}-\phi+1}{2\sqrt{2}}\) | \(\frac{\phi-1+\sqrt{4-\left(\phi-1\right)^{2}}}{2\sqrt{2}}\) | \(\frac{\sqrt{4-\left(\phi-1\right)^{2}}-\phi+1}{\phi-1+\sqrt{4-\left(\phi-1\right)^{2}}}\) | \(\frac{\phi-1+\sqrt{4-\left(\phi-1\right)^{2}}}{\sqrt{4-\left(\phi-1\right)^{2}}-\phi+1}\) | \(\frac{2\sqrt{2}}{\phi-1+\sqrt{4-\left(\phi-1\right)^{2}}}\) | \(\frac{2\sqrt{2}}{\sqrt{4-\left(\phi-1\right)^{2}}-\phi+1}\) |
| \(28^\circ\) | \(\frac{7\pi}{45}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n+1\right)!}\cdot\left(\frac{7\pi}{45}\right)^{2n+1}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n\right)!}\cdot\left(\frac{7\pi}{45}\right)^{2n}\) | \(\frac{\sin28^\circ}{\cos28^\circ}\) | \(\frac{\cos28^\circ}{\sin28^\circ}\) | \(\frac{1}{\cos28^\circ}\) | \(\frac{1}{\sin28^\circ}\) |
| \(29^\circ\) | \(\frac{29\pi}{180}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n+1\right)!}\cdot\left(\frac{29\pi}{180}\right)^{2n+1}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n\right)!}\cdot\left(\frac{29\pi}{180}\right)^{2n}\) | \(\frac{\sin29^\circ}{\cos29^\circ}\) | \(\frac{\cos29^\circ}{\sin29^\circ}\) | \(\frac{1}{\cos29^\circ}\) | \(\frac{1}{\sin29^\circ}\) |
| \(30^\circ\) | \(\frac{\pi}{6}\) | \(\frac{1}{2}\) | \(\frac{\sqrt{3}}{2}\) | \(\frac{1}{\sqrt{3}}\) | \(\sqrt{3}\) | \(\frac{2}{\sqrt{3}}\) | \(2\) |
| \(31^\circ\) | \(\frac{31\pi}{180}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n+1\right)!}\cdot\left(\frac{31\pi}{180}\right)^{2n+1}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n\right)!}\cdot\left(\frac{31\pi}{180}\right)^{2n}\) | \(\frac{\sin31^\circ}{\cos31^\circ}\) | \(\frac{\cos31^\circ}{\sin31^\circ}\) | \(\frac{1}{\cos31^\circ}\) | \(\frac{1}{\sin31^\circ}\) |
| \(32^\circ\) | \(\frac{8\pi}{45}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n+1\right)!}\cdot\left(\frac{8\pi}{45}\right)^{2n+1}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n\right)!}\cdot\left(\frac{8\pi}{45}\right)^{2n}\) | \(\frac{\sin32^\circ}{\cos32^\circ}\) | \(\frac{\cos32^\circ}{\sin32^\circ}\) | \(\frac{1}{\cos32^\circ}\) | \(\frac{1}{\sin32^\circ}\) |
| \(33^\circ\) | \(\frac{11\pi}{60}\) | \(\frac{\left(\sqrt{6}-\sqrt{2}\right)\sqrt{4-\left(\phi-1\right)^{2}}+\left(\sqrt{6}+\sqrt{2}\right)\left(\phi-1\right)}{8}\) | \(\frac{\left(\sqrt{6}+\sqrt{2}\right)\sqrt{4-\left(\phi-1\right)^{2}}-\left(\sqrt{6}-\sqrt{2}\right)\left(\phi-1\right)}{8}\) | \(\frac{\left(\sqrt{6}-\sqrt{2}\right)\sqrt{4-\left(\phi-1\right)^{2}}+\left(\sqrt{6}+\sqrt{2}\right)\left(\phi-1\right)}{\left(\sqrt{6}+\sqrt{2}\right)\sqrt{4-\left(\phi-1\right)^{2}}-\left(\sqrt{6}-\sqrt{2}\right)\left(\phi-1\right)}\) | \(\frac{\left(\sqrt{6}+\sqrt{2}\right)\sqrt{4-\left(\phi-1\right)^{2}}-\left(\sqrt{6}-\sqrt{2}\right)\left(\phi-1\right)}{\left(\sqrt{6}-\sqrt{2}\right)\sqrt{4-\left(\phi-1\right)^{2}}+\left(\sqrt{6}+\sqrt{2}\right)\left(\phi-1\right)}\) | \(\frac{8}{\left(\sqrt{6}+\sqrt{2}\right)\sqrt{4-\left(\phi-1\right)^{2}}-\left(\sqrt{6}-\sqrt{2}\right)\left(\phi-1\right)}\) | \(\frac{8}{\left(\sqrt{6}-\sqrt{2}\right)\sqrt{4-\left(\phi-1\right)^{2}}+\left(\sqrt{6}+\sqrt{2}\right)\left(\phi-1\right)}\) |
| \(34^\circ\) | \(\frac{17\pi}{90}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n+1\right)!}\cdot\left(\frac{17\pi}{90}\right)^{2n+1}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n\right)!}\cdot\left(\frac{17\pi}{90}\right)^{2n}\) | \(\frac{\sin34^\circ}{\cos34^\circ}\) | \(\frac{\cos34^\circ}{\sin34^\circ}\) | \(\frac{1}{\cos34^\circ}\) | \(\frac{1}{\sin34^\circ}\) |
| \(35^\circ\) | \(\frac{7\pi}{36}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n+1\right)!}\cdot\left(\frac{7\pi}{36}\right)^{2n+1}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n\right)!}\cdot\left(\frac{7\pi}{36}\right)^{2n}\) | \(\frac{\sin35^\circ}{\cos35^\circ}\) | \(\frac{\cos35^\circ}{\sin35^\circ}\) | \(\frac{1}{\cos35^\circ}\) | \(\frac{1}{\sin35^\circ}\) |
| \(36^\circ\) | \(\frac{\pi}{5}\) | \(\frac{\sqrt{4-\phi^{2}}}{2}\) | \(\frac{\phi}{2}\) | \(\frac{\sqrt{4-\phi^{2}}}{\phi}\) | \(\frac{\phi}{\sqrt{4-\phi^{2}}}\) | \(\frac{2}{\phi}\) | \(\frac{2}{\sqrt{4-\phi^{2}}}\) |
| \(37^\circ\) | \(\frac{37\pi}{180}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n+1\right)!}\cdot\left(\frac{37\pi}{180}\right)^{2n+1}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n\right)!}\cdot\left(\frac{37\pi}{180}\right)^{2n}\) | \(\frac{\sin37^\circ}{\cos37^\circ}\) | \(\frac{\cos37^\circ}{\sin37^\circ}\) | \(\frac{1}{\cos37^\circ}\) | \(\frac{1}{\sin37^\circ}\) |
| \(38^\circ\) | \(\frac{19\pi}{90}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n+1\right)!}\cdot\left(\frac{19\pi}{90}\right)^{2n+1}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n\right)!}\cdot\left(\frac{19\pi}{90}\right)^{2n}\) | \(\frac{\sin38^\circ}{\cos38^\circ}\) | \(\frac{\cos38^\circ}{\sin38^\circ}\) | \(\frac{1}{\cos38^\circ}\) | \(\frac{1}{\sin38^\circ}\) |
| \(39^\circ\) | \(\frac{13\pi}{60}\) | \(\frac{\left(\sqrt{6}-\sqrt{2}\right)\left(\phi+\sqrt{12-3\phi^{2}}\right)+\left(\sqrt{6}+\sqrt{2}\right)\left(\sqrt{3}\phi-\sqrt{4-\phi^{2}}\right)}{16}\) | \(\frac{\left(\sqrt{6}+\sqrt{2}\right)\left(\phi+\sqrt{12-3\phi^{2}}\right)+\left(\sqrt{6}-\sqrt{2}\right)\left(\sqrt{4-\phi^{2}}-\sqrt{3}\phi\right)}{16}\) | \(\frac{\left(\sqrt{6}-\sqrt{2}\right)\left(\phi+\sqrt{12-3\phi^{2}}\right)+\left(\sqrt{6}+\sqrt{2}\right)\left(\sqrt{3}\phi-\sqrt{4-\phi^{2}}\right)}{\left(\sqrt{6}+\sqrt{2}\right)\left(\phi+\sqrt{12-3\phi^{2}}\right)+\left(\sqrt{6}-\sqrt{2}\right)\left(\sqrt{4-\phi^{2}}-\sqrt{3}\phi\right)}\) | \(\frac{\left(\sqrt{6}+\sqrt{2}\right)\left(\phi+\sqrt{12-3\phi^{2}}\right)+\left(\sqrt{6}-\sqrt{2}\right)\left(\sqrt{4-\phi^{2}}-\sqrt{3}\phi\right)}{\left(\sqrt{6}-\sqrt{2}\right)\left(\phi+\sqrt{12-3\phi^{2}}\right)+\left(\sqrt{6}+\sqrt{2}\right)\left(\sqrt{3}\phi-\sqrt{4-\phi^{2}}\right)}\) | \(\frac{16}{\left(\sqrt{6}+\sqrt{2}\right)\left(\phi+\sqrt{12-3\phi^{2}}\right)+\left(\sqrt{6}-\sqrt{2}\right)\left(\sqrt{4-\phi^{2}}-\sqrt{3}\phi\right)}\) | \(\frac{16}{\left(\sqrt{6}-\sqrt{2}\right)\left(\phi+\sqrt{12-3\phi^{2}}\right)+\left(\sqrt{6}+\sqrt{2}\right)\left(\sqrt{3}\phi-\sqrt{4-\phi^{2}}\right)}\) |
| \(40^\circ\) | \(\frac{2\pi}{9}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n+1\right)!}\cdot\left(\frac{2\pi}{9}\right)^{2n+1}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n\right)!}\cdot\left(\frac{2\pi}{9}\right)^{2n}\) | \(\frac{\sin40^\circ}{\cos40^\circ}\) | \(\frac{\cos40^\circ}{\sin40^\circ}\) | \(\frac{1}{\cos40^\circ}\) | \(\frac{1}{\sin40^\circ}\) |
| \(41^\circ\) | \(\frac{41\pi}{180}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n+1\right)!}\cdot\left(\frac{41\pi}{180}\right)^{2n+1}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n\right)!}\cdot\left(\frac{41\pi}{180}\right)^{2n}\) | \(\frac{\sin41^\circ}{\cos41^\circ}\) | \(\frac{\cos41^\circ}{\sin41^\circ}\) | \(\frac{1}{\cos41^\circ}\) | \(\frac{1}{\sin41^\circ}\) |
| \(42^\circ\) | \(\frac{7\pi}{30}\) | \(\frac{\sqrt{12-3\left(\phi-1\right)^{2}}-\phi+1}{4}\) | \(\frac{\sqrt{3}\phi-\sqrt{3}+\sqrt{4-\left(\phi-1\right)^{2}}}{4}\) | \(\frac{\sqrt{12-3\left(\phi-1\right)^{2}}-\phi+1}{\sqrt{3}\phi-\sqrt{3}+\sqrt{4-\left(\phi-1\right)^{2}}}\) | \(\frac{\sqrt{3}\phi-\sqrt{3}+\sqrt{4-\left(\phi-1\right)^{2}}}{\sqrt{12-3\left(\phi-1\right)^{2}}-\phi+1}\) | \(\frac{4}{\sqrt{3}\phi-\sqrt{3}+\sqrt{4-\left(\phi-1\right)^{2}}}\) | \(\frac{4}{\sqrt{12-3\left(\phi-1\right)^{2}}-\phi+1}\) |
| \(43^\circ\) | \(\frac{43\pi}{180}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n+1\right)!}\cdot\left(\frac{43\pi}{180}\right)^{2n+1}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n\right)!}\cdot\left(\frac{43\pi}{180}\right)^{2n}\) | \(\frac{\sin43^\circ}{\cos43^\circ}\) | \(\frac{\cos43^\circ}{\sin43^\circ}\) | \(\frac{1}{\cos43^\circ}\) | \(\frac{1}{\sin43^\circ}\) |
| \(44^\circ\) | \(\frac{11\pi}{45}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n+1\right)!}\cdot\left(\frac{11\pi}{45}\right)^{2n+1}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n\right)!}\cdot\left(\frac{11\pi}{45}\right)^{2n}\) | \(\frac{\sin44^\circ}{\cos44^\circ}\) | \(\frac{\cos44^\circ}{\sin44^\circ}\) | \(\frac{1}{\cos44^\circ}\) | \(\frac{1}{\sin44^\circ}\) |
| \(45^\circ\) | \(\frac{\pi}{4}\) | \(\frac{1}{\sqrt{2}}\) | \(\frac{1}{\sqrt{2}}\) | \(1\) | \(1\) | \(\sqrt{2}\) | \(\sqrt{2}\) |
| \(46^\circ\) | \(\frac{23\pi}{90}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n+1\right)!}\cdot\left(\frac{23\pi}{90}\right)^{2n+1}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n\right)!}\cdot\left(\frac{23\pi}{90}\right)^{2n}\) | \(\frac{\sin46^\circ}{\cos46^\circ}\) | \(\frac{\cos46^\circ}{\sin46^\circ}\) | \(\frac{1}{\cos46^\circ}\) | \(\frac{1}{\sin46^\circ}\) |
| \(47^\circ\) | \(\frac{47\pi}{180}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n+1\right)!}\cdot\left(\frac{47\pi}{180}\right)^{2n+1}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n\right)!}\cdot\left(\frac{47\pi}{180}\right)^{2n}\) | \(\frac{\sin47^\circ}{\cos47^\circ}\) | \(\frac{\cos47^\circ}{\sin47^\circ}\) | \(\frac{1}{\cos47^\circ}\) | \(\frac{1}{\sin47^\circ}\) |
| \(48^\circ\) | \(\frac{4\pi}{15}\) | \(\frac{\sqrt{3}\phi-\sqrt{3}+\sqrt{4-\left(\phi-1\right)^{2}}}{4}\) | \(\frac{\sqrt{12-3\left(\phi-1\right)^{2}}-\phi+1}{4}\) | \(\frac{\sqrt{3}\phi-\sqrt{3}+\sqrt{4-\left(\phi-1\right)^{2}}}{\sqrt{12-3\left(\phi-1\right)^{2}}-\phi+1}\) | \(\frac{\sqrt{12-3\left(\phi-1\right)^{2}}-\phi+1}{\sqrt{3}\phi-\sqrt{3}+\sqrt{4-\left(\phi-1\right)^{2}}}\) | \(\frac{4}{\sqrt{12-3\left(\phi-1\right)^{2}}-\phi+1}\) | \(\frac{4}{\sqrt{3}\phi-\sqrt{3}+\sqrt{4-\left(\phi-1\right)^{2}}}\) |
| \(49^\circ\) | \(\frac{49\pi}{180}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n+1\right)!}\cdot\left(\frac{49\pi}{180}\right)^{2n+1}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n\right)!}\cdot\left(\frac{49\pi}{180}\right)^{2n}\) | \(\frac{\sin49^\circ}{\cos49^\circ}\) | \(\frac{\cos49^\circ}{\sin49^\circ}\) | \(\frac{1}{\cos49^\circ}\) | \(\frac{1}{\sin49^\circ}\) |
| \(50^\circ\) | \(\frac{5\pi}{18}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n+1\right)!}\cdot\left(\frac{5\pi}{18}\right)^{2n+1}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n\right)!}\cdot\left(\frac{5\pi}{18}\right)^{2n}\) | \(\frac{\sin50^\circ}{\cos50^\circ}\) | \(\frac{\cos50^\circ}{\sin50^\circ}\) | \(\frac{1}{\cos50^\circ}\) | \(\frac{1}{\sin50^\circ}\) |
| \(51^\circ\) | \(\frac{17\pi}{60}\) | \(\frac{\left(\sqrt{6}+\sqrt{2}\right)\left(\phi+\sqrt{12-3\phi^{2}}\right)+\left(\sqrt{6}-\sqrt{2}\right)\left(\sqrt{4-\phi^{2}}-\sqrt{3}\phi\right)}{16}\) | \(\frac{\left(\sqrt{6}-\sqrt{2}\right)\left(\phi+\sqrt{12-3\phi^{2}}\right)+\left(\sqrt{6}+\sqrt{2}\right)\left(\sqrt{3}\phi-\sqrt{4-\phi^{2}}\right)}{16}\) | \(\frac{\left(\sqrt{6}+\sqrt{2}\right)\left(\phi+\sqrt{12-3\phi^{2}}\right)+\left(\sqrt{6}-\sqrt{2}\right)\left(\sqrt{4-\phi^{2}}-\sqrt{3}\phi\right)}{\left(\sqrt{6}-\sqrt{2}\right)\left(\phi+\sqrt{12-3\phi^{2}}\right)+\left(\sqrt{6}+\sqrt{2}\right)\left(\sqrt{3}\phi-\sqrt{4-\phi^{2}}\right)}\) | \(\frac{\left(\sqrt{6}-\sqrt{2}\right)\left(\phi+\sqrt{12-3\phi^{2}}\right)+\left(\sqrt{6}+\sqrt{2}\right)\left(\sqrt{3}\phi-\sqrt{4-\phi^{2}}\right)}{\left(\sqrt{6}+\sqrt{2}\right)\left(\phi+\sqrt{12-3\phi^{2}}\right)+\left(\sqrt{6}-\sqrt{2}\right)\left(\sqrt{4-\phi^{2}}-\sqrt{3}\phi\right)}\) | \(\frac{16}{\left(\sqrt{6}-\sqrt{2}\right)\left(\phi+\sqrt{12-3\phi^{2}}\right)+\left(\sqrt{6}+\sqrt{2}\right)\left(\sqrt{3}\phi-\sqrt{4-\phi^{2}}\right)}\) | \(\frac{16}{\left(\sqrt{6}+\sqrt{2}\right)\left(\phi+\sqrt{12-3\phi^{2}}\right)+\left(\sqrt{6}-\sqrt{2}\right)\left(\sqrt{4-\phi^{2}}-\sqrt{3}\phi\right)}\) |
| \(52^\circ\) | \(\frac{13\pi}{45}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n+1\right)!}\cdot\left(\frac{13\pi}{45}\right)^{2n+1}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n\right)!}\cdot\left(\frac{13\pi}{45}\right)^{2n}\) | \(\frac{\sin52^\circ}{\cos52^\circ}\) | \(\frac{\cos52^\circ}{\sin52^\circ}\) | \(\frac{1}{\cos52^\circ}\) | \(\frac{1}{\sin52^\circ}\) |
| \(53^\circ\) | \(\frac{53\pi}{180}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n+1\right)!}\cdot\left(\frac{53\pi}{180}\right)^{2n+1}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n\right)!}\cdot\left(\frac{53\pi}{180}\right)^{2n}\) | \(\frac{\sin53^\circ}{\cos53^\circ}\) | \(\frac{\cos53^\circ}{\sin53^\circ}\) | \(\frac{1}{\cos53^\circ}\) | \(\frac{1}{\sin53^\circ}\) |
| \(54^\circ\) | \(\frac{3\pi}{10}\) | \(\frac{\phi}{2}\) | \(\frac{\sqrt{4-\phi^{2}}}{2}\) | \(\frac{\phi}{\sqrt{4-\phi^{2}}}\) | \(\frac{\sqrt{4-\phi^{2}}}{\phi}\) | \(\frac{2}{\sqrt{4-\phi^{2}}}\) | \(\frac{2}{\phi}\) |
| \(55^\circ\) | \(\frac{11\pi}{36}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n+1\right)!}\cdot\left(\frac{11\pi}{36}\right)^{2n+1}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n\right)!}\cdot\left(\frac{11\pi}{36}\right)^{2n}\) | \(\frac{\sin55^\circ}{\cos55^\circ}\) | \(\frac{\cos55^\circ}{\sin55^\circ}\) | \(\frac{1}{\cos55^\circ}\) | \(\frac{1}{\sin55^\circ}\) |
| \(56^\circ\) | \(\frac{14\pi}{45}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n+1\right)!}\cdot\left(\frac{14\pi}{45}\right)^{2n+1}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n\right)!}\cdot\left(\frac{14\pi}{45}\right)^{2n}\) | \(\frac{\sin56^\circ}{\cos56^\circ}\) | \(\frac{\cos56^\circ}{\sin56^\circ}\) | \(\frac{1}{\cos56^\circ}\) | \(\frac{1}{\sin56^\circ}\) |
| \(57^\circ\) | \(\frac{19\pi}{60}\) | \(\frac{\left(\sqrt{6}+\sqrt{2}\right)\sqrt{4-\left(\phi-1\right)^{2}}-\left(\sqrt{6}-\sqrt{2}\right)\left(\phi-1\right)}{8}\) | \(\frac{\left(\sqrt{6}-\sqrt{2}\right)\sqrt{4-\left(\phi-1\right)^{2}}+\left(\sqrt{6}+\sqrt{2}\right)\left(\phi-1\right)}{8}\) | \(\frac{\left(\sqrt{6}+\sqrt{2}\right)\sqrt{4-\left(\phi-1\right)^{2}}-\left(\sqrt{6}-\sqrt{2}\right)\left(\phi-1\right)}{\left(\sqrt{6}-\sqrt{2}\right)\sqrt{4-\left(\phi-1\right)^{2}}+\left(\sqrt{6}+\sqrt{2}\right)\left(\phi-1\right)}\) | \(\frac{\left(\sqrt{6}-\sqrt{2}\right)\sqrt{4-\left(\phi-1\right)^{2}}+\left(\sqrt{6}+\sqrt{2}\right)\left(\phi-1\right)}{\left(\sqrt{6}+\sqrt{2}\right)\sqrt{4-\left(\phi-1\right)^{2}}-\left(\sqrt{6}-\sqrt{2}\right)\left(\phi-1\right)}\) | \(\frac{8}{\left(\sqrt{6}-\sqrt{2}\right)\sqrt{4-\left(\phi-1\right)^{2}}+\left(\sqrt{6}+\sqrt{2}\right)\left(\phi-1\right)}\) | \(\frac{8}{\left(\sqrt{6}+\sqrt{2}\right)\sqrt{4-\left(\phi-1\right)^{2}}-\left(\sqrt{6}-\sqrt{2}\right)\left(\phi-1\right)}\) |
| \(58^\circ\) | \(\frac{29\pi}{90}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n+1\right)!}\cdot\left(\frac{29\pi}{90}\right)^{2n+1}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n\right)!}\cdot\left(\frac{29\pi}{90}\right)^{2n}\) | \(\frac{\sin58^\circ}{\cos58^\circ}\) | \(\frac{\cos58^\circ}{\sin58^\circ}\) | \(\frac{1}{\cos58^\circ}\) | \(\frac{1}{\sin58^\circ}\) |
| \(59^\circ\) | \(\frac{59\pi}{180}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n+1\right)!}\cdot\left(\frac{59\pi}{180}\right)^{2n+1}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n\right)!}\cdot\left(\frac{59\pi}{180}\right)^{2n}\) | \(\frac{\sin59^\circ}{\cos59^\circ}\) | \(\frac{\cos59^\circ}{\sin59^\circ}\) | \(\frac{1}{\cos59^\circ}\) | \(\frac{1}{\sin59^\circ}\) |
| \(60^\circ\) | \(\frac{\pi}{3}\) | \(\frac{\sqrt{3}}{2}\) | \(\frac{1}{2}\) | \(\sqrt{3}\) | \(\frac{1}{\sqrt{3}}\) | \(2\) | \(\frac{2}{\sqrt{3}}\) |
| \(61^\circ\) | \(\frac{61\pi}{180}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n+1\right)!}\cdot\left(\frac{61\pi}{180}\right)^{2n+1}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n\right)!}\cdot\left(\frac{61\pi}{180}\right)^{2n}\) | \(\frac{\sin61^\circ}{\cos61^\circ}\) | \(\frac{\cos61^\circ}{\sin61^\circ}\) | \(\frac{1}{\cos61^\circ}\) | \(\frac{1}{\sin61^\circ}\) |
| \(62^\circ\) | \(\frac{31\pi}{90}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n+1\right)!}\cdot\left(\frac{31\pi}{90}\right)^{2n+1}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n\right)!}\cdot\left(\frac{31\pi}{90}\right)^{2n}\) | \(\frac{\sin62^\circ}{\cos62^\circ}\) | \(\frac{\cos62^\circ}{\sin62^\circ}\) | \(\frac{1}{\cos62^\circ}\) | \(\frac{1}{\sin62^\circ}\) |
| \(63^\circ\) | \(\frac{7\pi}{20}\) | \(\frac{\phi-1+\sqrt{4-\left(\phi-1\right)^{2}}}{2\sqrt{2}}\) | \(\frac{\sqrt{4-\left(\phi-1\right)^{2}}-\phi+1}{2\sqrt{2}}\) | \(\frac{\phi-1+\sqrt{4-\left(\phi-1\right)^{2}}}{\sqrt{4-\left(\phi-1\right)^{2}}-\phi+1}\) | \(\frac{\sqrt{4-\left(\phi-1\right)^{2}}-\phi+1}{\phi-1+\sqrt{4-\left(\phi-1\right)^{2}}}\) | \(\frac{2\sqrt{2}}{\sqrt{4-\left(\phi-1\right)^{2}}-\phi+1}\) | \(\frac{2\sqrt{2}}{\phi-1+\sqrt{4-\left(\phi-1\right)^{2}}}\) |
| \(64^\circ\) | \(\frac{16\pi}{45}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n+1\right)!}\cdot\left(\frac{16\pi}{45}\right)^{2n+1}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n\right)!}\cdot\left(\frac{16\pi}{45}\right)^{2n}\) | \(\frac{\sin64^\circ}{\cos64^\circ}\) | \(\frac{\cos64^\circ}{\sin64^\circ}\) | \(\frac{1}{\cos64^\circ}\) | \(\frac{1}{\sin64^\circ}\) |
| \(65^\circ\) | \(\frac{13\pi}{36}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n+1\right)!}\cdot\left(\frac{13\pi}{36}\right)^{2n+1}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n\right)!}\cdot\left(\frac{13\pi}{36}\right)^{2n}\) | \(\frac{\sin65^\circ}{\cos65^\circ}\) | \(\frac{\cos65^\circ}{\sin65^\circ}\) | \(\frac{1}{\cos65^\circ}\) | \(\frac{1}{\sin65^\circ}\) |
| \(66^\circ\) | \(\frac{11\pi}{30}\) | \(\frac{\phi+\sqrt{12-3\phi^{2}}}{4}\) | \(\frac{\sqrt{3}\phi-\sqrt{4-\phi^{2}}}{4}\) | \(\frac{\phi+\sqrt{12-3\phi^{2}}}{\sqrt{3}\phi-\sqrt{4-\phi^{2}}}\) | \(\frac{\sqrt{3}\phi-\sqrt{4-\phi^{2}}}{\phi+\sqrt{12-3\phi^{2}}}\) | \(\frac{4}{\sqrt{3}\phi-\sqrt{4-\phi^{2}}}\) | \(\frac{4}{\phi+\sqrt{12-3\phi^{2}}}\) |
| \(67^\circ\) | \(\frac{67\pi}{180}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n+1\right)!}\cdot\left(\frac{67\pi}{180}\right)^{2n+1}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n\right)!}\cdot\left(\frac{67\pi}{180}\right)^{2n}\) | \(\frac{\sin67^\circ}{\cos67^\circ}\) | \(\frac{\cos67^\circ}{\sin67^\circ}\) | \(\frac{1}{\cos67^\circ}\) | \(\frac{1}{\sin67^\circ}\) |
| \(68^\circ\) | \(\frac{17\pi}{45}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n+1\right)!}\cdot\left(\frac{17\pi}{45}\right)^{2n+1}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n\right)!}\cdot\left(\frac{17\pi}{45}\right)^{2n}\) | \(\frac{\sin68^\circ}{\cos68^\circ}\) | \(\frac{\cos68^\circ}{\sin68^\circ}\) | \(\frac{1}{\cos68^\circ}\) | \(\frac{1}{\sin68^\circ}\) |
| \(69^\circ\) | \(\frac{23\pi}{60}\) | \(\frac{\left(\sqrt{6}-\sqrt{2}\right)\sqrt{4-\phi^{2}}+\phi\left(\sqrt{6}+\sqrt{2}\right)}{8}\) | \(\frac{\left(\sqrt{6}+\sqrt{2}\right)\sqrt{4-\phi^{2}}-\phi\left(\sqrt{6}-\sqrt{2}\right)}{8}\) | \(\frac{\left(\sqrt{6}-\sqrt{2}\right)\sqrt{4-\phi^{2}}+\phi\left(\sqrt{6}+\sqrt{2}\right)}{\left(\sqrt{6}+\sqrt{2}\right)\sqrt{4-\phi^{2}}-\phi\left(\sqrt{6}-\sqrt{2}\right)}\) | \(\frac{\left(\sqrt{6}+\sqrt{2}\right)\sqrt{4-\phi^{2}}-\phi\left(\sqrt{6}-\sqrt{2}\right)}{\left(\sqrt{6}-\sqrt{2}\right)\sqrt{4-\phi^{2}}+\phi\left(\sqrt{6}+\sqrt{2}\right)}\) | \(\frac{8}{\left(\sqrt{6}+\sqrt{2}\right)\sqrt{4-\phi^{2}}-\phi\left(\sqrt{6}-\sqrt{2}\right)}\) | \(\frac{8}{\left(\sqrt{6}-\sqrt{2}\right)\sqrt{4-\phi^{2}}+\phi\left(\sqrt{6}+\sqrt{2}\right)}\) |
| \(70^\circ\) | \(\frac{7\pi}{18}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n+1\right)!}\cdot\left(\frac{7\pi}{18}\right)^{2n+1}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n\right)!}\cdot\left(\frac{7\pi}{18}\right)^{2n}\) | \(\frac{\sin70^\circ}{\cos70^\circ}\) | \(\frac{\cos70^\circ}{\sin70^\circ}\) | \(\frac{1}{\cos70^\circ}\) | \(\frac{1}{\sin70^\circ}\) |
| \(71^\circ\) | \(\frac{71\pi}{180}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n+1\right)!}\cdot\left(\frac{71\pi}{180}\right)^{2n+1}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n\right)!}\cdot\left(\frac{71\pi}{180}\right)^{2n}\) | \(\frac{\sin71^\circ}{\cos71^\circ}\) | \(\frac{\cos71^\circ}{\sin71^\circ}\) | \(\frac{1}{\cos71^\circ}\) | \(\frac{1}{\sin71^\circ}\) |
| \(72^\circ\) | \(\frac{2\pi}{5}\) | \(\frac{\sqrt{4-\left(\phi-1\right)^{2}}}{2}\) | \(\frac{\phi-1}{2}\) | \(\frac{\sqrt{4-\left(\phi-1\right)^{2}}}{\phi-1}\) | \(\frac{\phi-1}{\sqrt{4-\left(\phi-1\right)^{2}}}\) | \(\frac{2}{\phi-1}\) | \(\frac{2}{\sqrt{4-\left(\phi-1\right)^{2}}}\) |
| \(73^\circ\) | \(\frac{73\pi}{180}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n+1\right)!}\cdot\left(\frac{73\pi}{180}\right)^{2n+1}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n\right)!}\cdot\left(\frac{73\pi}{180}\right)^{2n}\) | \(\frac{\sin73^\circ}{\cos73^\circ}\) | \(\frac{\cos73^\circ}{\sin73^\circ}\) | \(\frac{1}{\cos73^\circ}\) | \(\frac{1}{\sin73^\circ}\) |
| \(74^\circ\) | \(\frac{37\pi}{90}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n+1\right)!}\cdot\left(\frac{37\pi}{90}\right)^{2n+1}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n\right)!}\cdot\left(\frac{37\pi}{90}\right)^{2n}\) | \(\frac{\sin74^\circ}{\cos74^\circ}\) | \(\frac{\cos74^\circ}{\sin74^\circ}\) | \(\frac{1}{\cos74^\circ}\) | \(\frac{1}{\sin74^\circ}\) |
| \(75^\circ\) | \(\frac{5\pi}{12}\) | \(\frac{\sqrt{6}+\sqrt{2}}{4}\) | \(\frac{\sqrt{6}-\sqrt{2}}{4}\) | \(2+\sqrt{3}\) | \(2-\sqrt{3}\) | \(\sqrt{6}+\sqrt{2}\) | \(\sqrt{6}-\sqrt{2}\) |
| \(76^\circ\) | \(\frac{19\pi}{45}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n+1\right)!}\cdot\left(\frac{19\pi}{45}\right)^{2n+1}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n\right)!}\cdot\left(\frac{19\pi}{45}\right)^{2n}\) | \(\frac{\sin76^\circ}{\cos76^\circ}\) | \(\frac{\cos76^\circ}{\sin76^\circ}\) | \(\frac{1}{\cos76^\circ}\) | \(\frac{1}{\sin76^\circ}\) |
| \(77^\circ\) | \(\frac{77\pi}{180}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n+1\right)!}\cdot\left(\frac{77\pi}{180}\right)^{2n+1}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n\right)!}\cdot\left(\frac{77\pi}{180}\right)^{2n}\) | \(\frac{\sin77^\circ}{\cos77^\circ}\) | \(\frac{\cos77^\circ}{\sin77^\circ}\) | \(\frac{1}{\cos77^\circ}\) | \(\frac{1}{\sin77^\circ}\) |
| \(78^\circ\) | \(\frac{13\pi}{30}\) | \(\frac{\phi-1+\sqrt{12-3\left(\phi-1\right)^{2}}}{4}\) | \(\frac{\sqrt{4-\left(\phi-1\right)^{2}}-\sqrt{3}\phi+\sqrt{3}}{4}\) | \(\frac{\phi-1+\sqrt{12-3\left(\phi-1\right)^{2}}}{\sqrt{4-\left(\phi-1\right)^{2}}-\sqrt{3}\phi+\sqrt{3}}\) | \(\frac{\sqrt{4-\left(\phi-1\right)^{2}}-\sqrt{3}\phi+\sqrt{3}}{\phi-1+\sqrt{12-3\left(\phi-1\right)^{2}}}\) | \(\frac{4}{\sqrt{4-\left(\phi-1\right)^{2}}-\sqrt{3}\phi+\sqrt{3}}\) | \(\frac{4}{\phi-1+\sqrt{12-3\left(\phi-1\right)^{2}}}\) |
| \(79^\circ\) | \(\frac{79\pi}{180}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n+1\right)!}\cdot\left(\frac{79\pi}{180}\right)^{2n+1}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n\right)!}\cdot\left(\frac{79\pi}{180}\right)^{2n}\) | \(\frac{\sin79^\circ}{\cos79^\circ}\) | \(\frac{\cos79^\circ}{\sin79^\circ}\) | \(\frac{1}{\cos79^\circ}\) | \(\frac{1}{\sin79^\circ}\) |
| \(80^\circ\) | \(\frac{4\pi}{9}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n+1\right)!}\cdot\left(\frac{4\pi}{9}\right)^{2n+1}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n\right)!}\cdot\left(\frac{4\pi}{9}\right)^{2n}\) | \(\frac{\sin80^\circ}{\cos80^\circ}\) | \(\frac{\cos80^\circ}{\sin80^\circ}\) | \(\frac{1}{\cos80^\circ}\) | \(\frac{1}{\sin80^\circ}\) |
| \(81^\circ\) | \(\frac{9\pi}{20}\) | \(\frac{\sqrt{4-\phi^{2}}+\phi}{2\sqrt{2}}\) | \(\frac{\phi-\sqrt{4-\phi^{2}}}{2\sqrt{2}}\) | \(\frac{\sqrt{4-\phi^{2}}+\phi}{\phi-\sqrt{4-\phi^{2}}}\) | \(\frac{\phi-\sqrt{4-\phi^{2}}}{\sqrt{4-\phi^{2}}+\phi}\) | \(\frac{2\sqrt{2}}{\phi-\sqrt{4-\phi^{2}}}\) | \(\frac{2\sqrt{2}}{\sqrt{4-\phi^{2}}+\phi}\) |
| \(82^\circ\) | \(\frac{41\pi}{90}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n+1\right)!}\cdot\left(\frac{41\pi}{90}\right)^{2n+1}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n\right)!}\cdot\left(\frac{41\pi}{90}\right)^{2n}\) | \(\frac{\sin82^\circ}{\cos82^\circ}\) | \(\frac{\cos82^\circ}{\sin82^\circ}\) | \(\frac{1}{\cos82^\circ}\) | \(\frac{1}{\sin82^\circ}\) |
| \(83^\circ\) | \(\frac{83\pi}{180}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n+1\right)!}\cdot\left(\frac{83\pi}{180}\right)^{2n+1}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n\right)!}\cdot\left(\frac{83\pi}{180}\right)^{2n}\) | \(\frac{\sin83^\circ}{\cos83^\circ}\) | \(\frac{\cos83^\circ}{\sin83^\circ}\) | \(\frac{1}{\cos83^\circ}\) | \(\frac{1}{\sin83^\circ}\) |
| \(84^\circ\) | \(\frac{7\pi}{15}\) | \(\frac{\sqrt{3}\phi+\sqrt{4-\phi^{2}}}{4}\) | \(\frac{\sqrt{12-3\phi^{2}}-\phi}{4}\) | \(\frac{\sqrt{3}\phi+\sqrt{4-\phi^{2}}}{\sqrt{12-3\phi^{2}}-\phi}\) | \(\frac{\sqrt{12-3\phi^{2}}-\phi}{\sqrt{3}\phi+\sqrt{4-\phi^{2}}}\) | \(\frac{4}{\sqrt{12-3\phi^{2}}-\phi}\) | \(\frac{4}{\sqrt{3}\phi+\sqrt{4-\phi^{2}}}\) |
| \(85^\circ\) | \(\frac{17\pi}{36}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n+1\right)!}\cdot\left(\frac{17\pi}{36}\right)^{2n+1}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n\right)!}\cdot\left(\frac{17\pi}{36}\right)^{2n}\) | \(\frac{\sin85^\circ}{\cos85^\circ}\) | \(\frac{\cos85^\circ}{\sin85^\circ}\) | \(\frac{1}{\cos85^\circ}\) | \(\frac{1}{\sin85^\circ}\) |
| \(86^\circ\) | \(\frac{43\pi}{90}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n+1\right)!}\cdot\left(\frac{43\pi}{90}\right)^{2n+1}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n\right)!}\cdot\left(\frac{43\pi}{90}\right)^{2n}\) | \(\frac{\sin86^\circ}{\cos86^\circ}\) | \(\frac{\cos86^\circ}{\sin86^\circ}\) | \(\frac{1}{\cos86^\circ}\) | \(\frac{1}{\sin86^\circ}\) |
| \(87^\circ\) | \(\frac{29\pi}{60}\) | \(\frac{\left(\phi-1\right)\left(\sqrt{6}-\sqrt{2}\right)+\left(\sqrt{6}+\sqrt{2}\right)\sqrt{4-\left(\phi-1\right)^{2}}}{8}\) | \(\frac{\left(\phi-1\right)\left(\sqrt{6}+\sqrt{2}\right)-\left(\sqrt{6}-\sqrt{2}\right)\sqrt{4-\left(\phi-1\right)^{2}}}{8}\) | \(\frac{\left(\phi-1\right)\left(\sqrt{6}-\sqrt{2}\right)+\left(\sqrt{6}+\sqrt{2}\right)\sqrt{4-\left(\phi-1\right)^{2}}}{\left(\phi-1\right)\left(\sqrt{6}+\sqrt{2}\right)-\left(\sqrt{6}-\sqrt{2}\right)\sqrt{4-\left(\phi-1\right)^{2}}}\) | \(\frac{\left(\phi-1\right)\left(\sqrt{6}+\sqrt{2}\right)-\left(\sqrt{6}-\sqrt{2}\right)\sqrt{4-\left(\phi-1\right)^{2}}}{\left(\phi-1\right)\left(\sqrt{6}-\sqrt{2}\right)+\left(\sqrt{6}+\sqrt{2}\right)\sqrt{4-\left(\phi-1\right)^{2}}}\) | \(\frac{8}{\left(\phi-1\right)\left(\sqrt{6}+\sqrt{2}\right)-\left(\sqrt{6}-\sqrt{2}\right)\sqrt{4-\left(\phi-1\right)^{2}}}\) | \(\frac{8}{\left(\phi-1\right)\left(\sqrt{6}-\sqrt{2}\right)+\left(\sqrt{6}+\sqrt{2}\right)\sqrt{4-\left(\phi-1\right)^{2}}}\) |
| \(88^\circ\) | \(\frac{22\pi}{45}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n+1\right)!}\cdot\left(\frac{22\pi}{45}\right)^{2n+1}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n\right)!}\cdot\left(\frac{22\pi}{45}\right)^{2n}\) | \(\frac{\sin88^\circ}{\cos88^\circ}\) | \(\frac{\cos88^\circ}{\sin88^\circ}\) | \(\frac{1}{\cos88^\circ}\) | \(\frac{1}{\sin88^\circ}\) |
| \(89^\circ\) | \(\frac{89\pi}{180}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n+1\right)!}\cdot\left(\frac{89\pi}{180}\right)^{2n+1}\) | \(\sum_{n=0}^{\infty}\frac{\left(-1\right)^{n}}{\left(2n\right)!}\cdot\left(\frac{89\pi}{180}\right)^{2n}\) | \(\frac{\sin89^\circ}{\cos89^\circ}\) | \(\frac{\cos89^\circ}{\sin89^\circ}\) | \(\frac{1}{\cos89^\circ}\) | \(\frac{1}{\sin89^\circ}\) |
| \(90^\circ\) | \(\frac{\pi}{2}\) | \(1\) | \(0\) | \(\text{undefined}\) | \(0\) | \(\text{underfined}\) | \(1\) |
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