Ucale

# Some Important Trigonometric Values

The values of trigonometrical ratios ofÂ  angles are very important to solve the trigonometrical problems.

1. $\displaystyle \sin { { 15 }^{ o } } =\frac { \sqrt { 3 } -1 }{ 2\sqrt { 2 } }$
2. $\displaystyle \cos { { 15 }^{ o } } =\frac { \sqrt { 3 } +1 }{ 2\sqrt { 2 } }$
3. $\displaystyle \tan { { 15 }^{ o } } =2-\sqrt { 3 } =\cot { { 75 }^{ o } }$
4. $\displaystyle \cot { { 15 }^{ o } } =2+\sqrt { 3 } =\tan { { 75 }^{ o } }$
5. $\displaystyle \cos { { 22\frac { 1 }{ 2 } }^{ o } } =\frac { 1 }{ 2 } \left( \sqrt { 2+\sqrt { 2 } } \right)$
6. $\displaystyle \sin { { 22\frac { 1 }{ 2 } }^{ o } } =\frac { 1 }{ 2 } \left( \sqrt { 2-\sqrt { 2 } } \right)$
7. $\displaystyle \tan { { 22\frac { 1 }{ 2 } }^{ o } } =\sqrt { 2 } -1$
8. $\displaystyle \cot { { 22\frac { 1 }{ 2 } }^{ o } } =\sqrt { 2 } +1$
9. $\displaystyle \sin { { 18 }^{ o } } =\frac { \sqrt { 5 } -1 }{ 4 } =\cos { { 72 }^{ o } }$
10. $\displaystyle \cos { { 18 }^{ o } } =\frac { \sqrt { 10+2\sqrt { 5 } } }{ 4 } =\sin { { 72 }^{ o } }$
11. $\displaystyle \sin { { 36 }^{ o } } =\frac { \sqrt { 10-2\sqrt { 5 } } }{ 4 } =\cos { { 54 }^{ o } }$
12. $\displaystyle \cos { { 36 }^{ o } } =\frac { \sqrt { 5 } +1 }{ 4 } =\sin { { 54 }^{ o } }$
13. $\displaystyle \cos { { 9 }^{ o } } =\frac { \sqrt { 3+\sqrt { 5 } } +\sqrt { 5-\sqrt { 5 } } }{ 4 } =\sin { { 81 }^{ o } }$
14. $\displaystyle \sin { { 9 }^{ o } } =\frac { \sqrt { 3+\sqrt { 5 } } -\sqrt { 5-\sqrt { 5 } } }{ 4 } =\cos { { 81 }^{ o } }$
15. $\displaystyle \cos { { 36 }^{ o } } -\cos { { 72 }^{ o } } =\frac { 1 }{ 2 }$
16. $\displaystyle \cos { { 36 }^{ o } } .\cos { { 72 }^{ o } } =\frac { 1 }{ 4 }$
February 22, 2019
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