Need one example solving trigonometry.

Question

Calculate $\sin \beta, \tan \beta, \cot \beta, \cos(2\beta)$ if $\cos \beta = {5 \over 13}$ and $\beta \in (0^{\circ},90^{\circ})$.

I'm a student and I forgot how to solve it correctly...I need just one example. Thanks.

Answer 1

There are many ways:-

1. Try making a triangle and use $5$ as length of base and $13$ as length of Hypotenuse.
   [Hint: $5^2 +12^2 = 13^2$]
2. $\cos \beta = 5/13$ apply $\sin^2 \beta + \cos^2 \beta = 1$
3. For $\cos (2 \beta)$ use $\cos(2 \beta)= 2\cos^2 \beta -1$