Question

How do you find the values of the other trigonometric functions of theta from the information given `tan theta = −3`, and `sin theta > 0`?

Answer 1

Call tan x = t = -3, Use the trig identity: `cos^2 x = 1/(1 + t^2)`
Since tan x = -3 is negative and sin x > 0, then x should be in quadrant II

`cos^2 x = 1/(1 + 9) = 1/10 = 0.10 -> cos x = -0.316` (Quadrant II)

`sin^2 x = 1 - cos^2 x = 1 - 0.10 = 0.90 -> sin x = 0.95` (Quadrant II)

cot x = - 1/3

`sec = 1/cos x = 1/(-0.316) = -3.16`

`csc = 1/ sin x = 1/0.95 = 1.05`