How do you find tan -555?

1 Answer
Nghi N
Apr 10, 2018

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)

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