Question

How do you calculate `cos [Sin^-1 (-1/5) ]`?

Answer 1

In this way:

we have to calculate `cosalpha`, where

`alpha=sin^-1(-1/5)`,

`sinalpha=-1/5`.

Since the range of the function `y=sin^-1x` is an angle in the first and fourth quadrant, and since the value is negative, the angle `alpha` is in the fourth quadrant, and there the function cosine is positive, so:

`cosalpha=+sqrt(1-sin^2alpha)=sqrt(1-1/25)=sqrt(24/25)=2/5sqrt6`.