How do you find the remaining 5 trig functions of theta if cos(theta) = -1/3 and it is located in quadrant 3?

1 Answer
Nghi N.
Oct 17, 2015

Find 5 trig functions of x knowing cos x = - 1/3

Explanation:

cos x = - 1/3 --> cos^2 x = 1/9
sin^2 x = 1 - 1/9 = 8/9 --> sin x = +- 2sqrt2/3.
Since x is in Quadrant 3 #, its sin is negative.

tan x = (sin)/(cos) = (-1/3)(-3/sqrt2) = 1/sqrt2 = sqrt2
cot x = 1/(tan) = 1/sqrt2 = sqrt2/2
sec x = 1/(cos) = -3
csc x = 1/(sin) = - 3/2sqrt2 = - (3sqrt2)/4

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