If θ is an angle in standard position and its terminal side passes through the point (8,9), find the exact value of θ in simplest radical form.

Answer 1

(8,9) is a point with x=8 = adjacent side, y=9 = opposite side

hypotenuse = sqr(8^2 + 9^2) = sqr(64+81) = sqr(145) = about 12.04

The angle = tan^-1(9/8) = about 48.37 degrees

but you want exact radical form?

tan(theta) = opposite side/adjacent side = 9/8

Theta = tan^-1(9/8)