Question

Find the value of `cos(sin^-1(sqrt3/2))`?

Answer 1

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

Explanation:

`sin^-1x` means an angle whose sine ratio is `x`. If angle is `A`, then it means `sinA=x`.

Further, although there may be number of values of `A`, for whom sine is `x` - as all trigonometric ratios have a cycle of `2pi` radians, the range for inverse ratios is limited. While for sine, tangent, cosecant and cotangent range is `[-pi/2.pi/2]`, range for cosine and secant ratios, it is `[0,pi]`.

As `sin(pi/3)=sqrt3/2`, we have `sin^-1(sqrt3/2)=pi/3` or `60^o`

and `cos(sin^-1(sqrt3/2))=cos(pi/3)=1/2`

Note: It does not matter, whether we write angle in radians or degrees as irrespective of unit used, cosine is a ratio and

even `cos(sin^-1(sqrt3/2))=cos60^o=1/2`