Question

use the fact that the trigonometric functions are periodic to find the exact value of the given expression. do not use a calculator. tan 420

Answer 1

tan 420 = tan (360 + 60)

tan (x+y)= (tan x+tan y)/(1-tan x * tan y)

tan(360+60) = (tan 360 + tan 60)/(1-tan 360 * tan 60)

tan 360 = 0
tan 60 = sqrt(3)

plug in values in above eqn

=(0 + sqrt(3) ) / (1 - 0*sqrt(3))

=sqrt(3)/1

=sqrt(3)

Answer 2

trigonometric functions are periodic

so tan 420 = tan (420-360) = tan 60 = sqrt (3)