# How do you find the exact value of the half angle of #tan 157.5#?

##### 1 Answer

Apr 28, 2015

Use the trig identity:

Call tan x = t. Calculator gives:

d^2 = b^2 - 4ac = 4 + 0.67 = 4.67 -> d = 2.16

x1 = 2/0.82 + 2.16/0.82 = 5.07

x2 = 2/0.82 - 2.16/0.82 = -0.20 (rejected since tan x = tan (157.5/2) must be positive).

Answer: t = tan x = 5.07 --> x = 78.84