# How do you evaluate sin(arctan(2))?

May 21, 2015

Call x the $\left(a r c \left(\tan 2\right)\right)$. Calculator gives:

tan x = 2 --> $x = 63.43 \mathrm{de} g$

The trig unit circle gives another arc x that has the same tan value:

x = 63.43 + 180 = $243.43 \mathrm{de} g$

a. $\sin x = \sin \left(63 , 43\right) = 0.89$

b. $\sin x = \sin \left(243.43\right) = - \sin \left(63.43\right) = - 0.89$