CPM Homework Help : PCT Problem 4-40

If $\text{sin }θ =\frac { 5 } { 13 }$ and $\frac { \pi } { 2 }≤ θ ≤ \pi$ , find $\text{cos }θ$ and $\text{tan }θ$ .

Hint 1:

Draw and label a right triangle in the correct quadrant.

Hint 2:

Calculate the length of the unknown side.
(Or you may know it because it is a Pythagorean Triple!) When you label it, think about if it should be positive or negative.

Hint 3:

From the side lengths, you can find the $\text{cos}(θ)$ and the $\text{tan}(θ)$ .

Right triangle in third quadrant, horizontal leg on negative x axis, vertical leg on left labeled 5, hypotenyuse labeled 13.