If P is in quadrant 4 and x = 1/3 how do you evaluate the six trig functions of theta?

1 Answer
Nghi N.
Dec 3, 2015

Evaluate 6 trig function values

Explanation:

x = 1/3 and the radius of unit circle is 1, therefor
cos x = 1/3 --> x = - 70^@53. (Quadrant IV)
sin^2 x = 1 - cos^2 x = 1 - 1/9 = 8/9 --> sin x = +- (2sqrt2)/3
Since arc x is in Quadrant IV, then sin x = -sqrt2/3
tan x = sin x/(cos x) = (-sqrt2/3)(3/1) = -sqrt2
cot x = 1/(tan x) = -1/sqrt2 = -sqrt2/2
sec x = 1/(cos x) = 3
csc x = 1/(sin x) = - 3/(2sqrt2) = - (3sqrt2)/4

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