Find the values of the indicated functions Given tan 2 find

Find the values of the indicated functions.

Given tan =2, find sin and cos.

Solution

tan theta = 2

tan theta = perpendicular / base

perpendicular = 2

base = 1

hypotenuse = sqrt ( 2^2 + 1^2 ) by pythagorean identity

hypotenuse = sqrt 5

sin theta = perpendicular / hypotenuse = 2 / sqrt 5 = 2 sqrt 5 / 5

cos theta = base / hypotenuse = 1 / sqrt 5 = sqrt 5 / 5