Question

Evaluate sin(sin^-1 √3/2) and assume that all angles are in Quadrant I.

Answer 1

B)
`(√(3))/(2)`.

Explanation:

Given :
`sin(sin^(-1)((√(3))/(2))`.

To find : Evaluate.

Solution : We have given

`sin(sin^(-1)((√(3))/(2))`.

By the identity :
`sin(sin^(-1)(x)` = x .

Here, x =
`(√(3))/(2)`.

So,
`sin(sin^(-1)((√(3))/(2))` =
`(√(3))/(2)`.

Therefore, B)
`(√(3))/(2)`.

Answer 2

B. √3/2

Explanation:

Sin[sin⁻¹ (√3/2)]

sin⁻¹ (√3/2 = 60°

60° is the acute angle, in the first quadrant

Therefore;

Sin[sin⁻¹ (√3/2)] = sin 60° ; since sin⁻¹ (√3/2 = 60°

Sin 60° = √3/2

Therefore, the answer = √3/2