CPM Homework Help : CCA2 Problem 12-100

If $π ≤ θ ≤ \frac { 3 \pi } { 2 }$ and sin $θ = -\frac { 3 } { 5 }$ , find $\cosθ$ . Use what you know about the Pythagorean Identity and the unit circle to get started.

Hint:

Remember that the Pythagorean Identity is $\sin^2(θ)+\cos^2\left(θ\right)=1$ .
Try substituting the given value of $\sin(θ)$ into the equation, then solve for $\cos(θ)$ .

Step 1:

$\left(-\frac{3}{5}\right)^2+\cos\left(θ\right)=1$

Step 2:

$\cos^2\left(\theta\right)=\frac{16}{25}$

Step 3:

Take the square root of both sides to solve for $\cos\left(θ\right)$ .
Now use the unit circle to decide what the correct sign of the answer is.

Answer:

$-\frac{4}{5}$