Question

Find the exact value of cos(arcsin(1/4)). For full credit, explain your reasoning.

Answer 1

First way
arcsin(1/4) means that 1/4 sin of the angle.

sin(α)=1/4
sin²α+cos²α=1
(1/4)²+cos²α=1
cos²α=1-1/16 =15/16
cosα=+/-(√15)/4

Second way

sin(α)=1/4 =opposite leg/hipotenuse
cos(α)=adjacent leg/hypothenuse
adjacent leg =√(hypotenuse²- Opposite²)=√(16-1)=√15
cosα=+/-√15/4

For one value of sinα, possible 2 values of cosα.