Question

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

Answer 1

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`