Question

How do you evaluate `Cos(Arc sin (5/13))`?

Answer 1

`+-12/13`

Explanation:

Let `a = arc sin (5/13)`. Then, `sin a = 5/13 > 0`. a is in either 1st

quadrant or in the 2nd. Accordingly, the given expression

`cos a=+-sqrt(1-sin^2 a)=+-sqrt(1-5^2/13^2)=+-12/13`,

The negative value is from `sin (pi-a)=sin a = 5/13 and cos(pi-a)=-cos a`.

This is off, if arc sin (5/13) is restricted to be the principal value in

`[-pi/2, pi/2]`.