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