Question

How do you find the exact value of `cos(sin^-1 (1/2))`?

Answer 1

`:.cos(sin^-1(1/2)) =sqrt3/2`

Explanation:

Let `sin^-1(1/2)=theta :.sintheta=1/2` We know `sintheta`=(Perpendicular/Hypotenuse). Here perpendicular=1 , hypotenuse=2. : `:.Base = sqrt (h^2-p^2) =sqrt(4-1) =sqrt 3 :. cos theta= b/h=sqrt3/2 :. theta=cos^-1 sqrt(3/2)`
`:.cos(sin^-1(1/2)) = cos(cos^-1(sqrt3/2)) =sqrt3/2`[Ans]