# How do you find the values of the trigonometric functions of θ from the information given cot θ = 1/4, sin θ < 0?

##### 1 Answer

First of all,

The problem says that sine is negative and we can see above that tangent is negative. Using the C-A-S-T sign rule, we determine that

We know that

We use pythagorean theorem to find the hypotenuse.

However, the hypotenuse can never be negative, so we only keep

We can now fill in all four of the other ratios:

Hopefully this helps!