### Home > PC > Chapter 6 > Lesson 6.2.3 > Problem6-95

6-95.

Suppose $α$ is an angle in Quadrant I and $β$ is an angle in Quadrant IV such that $\sin α = \frac { 2 } { 3 }$ and $\cos β =\frac { 1 } { 4 }$.

1. Find the exact value of $\cos α$.

Draw diagrams. Find the 3rd side for each triangle.

Find the exact value of $\sin β$.

Draw diagrams. Find the 3rd side for each triangle.

2. Find the exact value of $\sin \left(α + β\right)$.

Use the angle sum and difference formula for the sine.

$\frac{2-5\sqrt{3}}{12}$

3. Find the exact value of $\cos \left(α + β\right)$.

Use the angle sum and difference formula for the cosine.