Ucale

# Some Important Trigonometric Values

The values of trigonometrical ratios of  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
Which class you are presently in?
Choose an option. You can change your option at any time.
You will be solving questions and growing your critical thinking skills.