How do you find tan -555?

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How do you find tan -555?

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Answer 1 · 2018-04-10T16:42:50

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: $tan 2 t = \frac{2 tan t}{1 - {tan}^{2} t} .$ $tan 2t = (2tan t)/(1 - tan^2 t).$
Call tan 15 = t --> $tan 2 t = tan 30 = \frac{1}{\sqrt{3}}$ $tan 2t = tan 30 = 1/sqrt3$ .
In this case:
$\frac{1}{\sqrt{3}} = 2 \frac{t}{1 - t^{2}}$ $1/sqrt3 = 2t/(1 - t^2)$ --> $- t^{2} + 1 = 2 \sqrt{3} t$ $- t^2 + 1 = 2sqrt3t$ , or
$t^{2} + 2 s q t 3 t - 1 = 0$ $t^2 + 2sqt3t - 1 = 0$
$D = d^{2} = 12 + 4 = 16$ $D = d^2 = 12 + 4 = 16$ --> $d = \pm 4$ $d = +- 4$
$tan 15 = t = - \sqrt{3} \pm 2$ $tan 15 = t = - sqrt3 +- 2$ --> 2 solutions -->
$tan 15 = - \sqrt{3} + 2 = 0.268$ $tan 15 = - sqrt3 + 2 = 0.268$
$tan 15 = - 2 q r t 3 - 2 = - 3.72$ $tan 15 = - 2qrt3 - 2 = - 3.72$ (Rejected because tan 15 is positive)

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How do you find tan -555?

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