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

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.