Question

How do you simplify `cos(arcsin(1/3))`?

Answer 1

`cos(arcsin(1/3))=(2sqrt2)/3`

Explanation:

`arcsinx` is the angle `theta` for which `sintheta=1/3`

or `theta=arcsin(1/3)`

As `sintheta=1/3`, `costheta=sqrt(1-(1/3)^2)=sqrt(8/9)=(2sqrt2)/3`

Now as `costheta=(2sqrt2)/3` and `theta=arcsin(1/3)`

`cos(arcsin(1/3))=(2sqrt2)/3`