### Home > PC3 > Chapter 11 > Lesson 11.2.3 > Problem11-118

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:

1. $\cos(α)$

1. $\sin(β)$

1. $\sin(α + β)$

$\sin(\text{A} + \text{B}) = \sin(\text{A})\cos(\text{B}) + \sin(B)\cos(\text{A})$

1. $\cos(α + β)$

$\cos(\text{A} + B) = \cos(\text{A})\cos(\text{B}) − \sin(\text{A})\sin(\text{B})$