Question

How do you find tan -555?

Answer 1

0.268

Explanation:

Unit circle gives -->
tan (-555) = tan (-15 - 540) = tan (-15 - 180) = - tan 15
Calculator gives -->
tan 15 = 0.268
tan (-555) = - tan 15 = - 0.268
Note 1. We can use calculator to directly obtain tan (-555)
tan (-555) = - tan 15 = 0.268.
Note 2. We can evaluate to get exact value of tan (-555)by using trig identity: `tan 2t = (2tan t)/(1 - tan^2 t).`
Call tan 15 = t --> `tan 2t = tan 30 = 1/sqrt3`.
In this case:
`1/sqrt3 = 2t/(1 - t^2)` --> `- t^2 + 1 = 2sqrt3t`, or
`t^2 + 2sqt3t - 1 = 0`
`D = d^2 = 12 + 4 = 16` --> `d = +- 4`
`tan 15 = t = - sqrt3 +- 2` --> 2 solutions -->
`tan 15 = - sqrt3 + 2 = 0.268`
`tan 15 = - 2qrt3 - 2 = - 3.72` (Rejected because tan 15 is positive)