# #40 5.05 Precalculus questions

Anonymous
timer Asked: May 15th, 2015
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### Question Description

Borys_S
School: Carnegie Mellon University

165° = pi - 15° and sin(165°) = sin(15°) > 0, cos(165°) = -cos(15°) < 0.

Let's find sin and cos of 15°, 15° is a half of 30°. sin(30°) = 1/2, cos(30°) = sqrt(3)/2.

By the half-angle formulas
(cos(15°))^2 = (1+cos(30°))/2 = (2+sqrt(3))/4,
(sin(15°))^2 = (1-cos(30°))/2 = (2-sqrt(3))/4.

So
cos(165°) = -cos(15°) = -sqrt(2+sqrt(3))/2,
sin(165°) = sin(15°) = sqrt(2-sqrt(3))/2,
tan(165°) = sin(165°)/cos(165°) = -sqrt(2-sqrt(3))/sqrt(2+sqrt(3)).

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Anonymous
Good stuff. Would use again.

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