Question

How do you calculate the `cos[2 sin^ -1 (1/2)]`?

Answer 1

`1/2`

Explanation:

First, focus on just `sin^-1(1/2)`. This is another way of asking, for what angle is sine equal to `"1/2"`? Recall that

`sin(pi/6)=1/2`

Thus, since `sin` and `arcsin` are inverse functions,

`sin^-1(1/2)=pi/6`

Substitute this into the original expression:

`cos[2sin^-1(1/2)]=cos(2*pi/6)=cos(pi/3)=1/2`