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 $\cos α$.

   Hint (a):

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

   Find the exact value of $\sin β$.

   Hint (b):

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

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

   Hint (c):

   Use the angle sum and difference formula for the sine.

   Answer (c):

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

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

   Hint (d):

   Use the angle sum and difference formula for the cosine.

4. Use your calculator to approximate your answer to part (d).