Question

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

Answer 1

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`