### Home > CCA2 > Chapter 12 > Lesson 12.2.1 > Problem12-100

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.

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 $\cos(θ)$.

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

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

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.

$-\frac{4}{5}$