Find the exact value of the expression Hint Sketch a right t

Find the exact value of the expression. (Hint: Sketch a right triangle.) cos(arcsin 20/29)

Solution

cos ( arc sin 20/29)

let arc sin 20/29 = x

so, sin x = 20/29 = perpendicular / hypotenuse

base = sqrt (hypotenuse^2 - perpendicular^2) = 29^2 - 20^2 = 21

therefore,

cos x = base / hypotenuse = 21/29

cos(arcsin 20/29)= 21/29