CPM Homework Help : PC3 Problem 11-118

Suppose $α$ is an angle in Quadrant I and $β$ is an angle in Quadrant IV such that $\sin(α) = \frac { 2 } { 3 }$ and $\cos(β) = \frac { 1 } { 4 }$ . Determine the exact value of:

$\cos(α)$
Hint (a):

$\sin(β)$
Hint (b):

$\sin(α + β)$
Hint (c):
$\sin(\text{A} + \text{B}) = \sin(\text{A})\cos(\text{B}) + \sin(B)\cos(\text{A})$

$\cos(α + β)$
Hint (d):
$\cos(\text{A} + B) = \cos(\text{A})\cos(\text{B}) − \sin(\text{A})\sin(\text{B})$