### Home > PC > Chapter 4 > Lesson 4.3.1 > Problem4-124

4-124.

Find all values of $θ$ that satisfy the equations below. Assume $0 ≤ θ ≤ 2\pi$. Use exact values.

1. $\text{sin }θ =-\frac { 1 } { 2 }$

Draw a unit circle. In which quadrants is sine negative?

1. $\text{cos }θ =\frac { \sqrt { 2 } } { 2 }$

1. What special angle is this?
2. In which quadrants is cosine positive?

1. $\text{tan }θ =\sqrt { 3 }$

$\tan(\theta)=\frac{\sin(\theta)}{\cos(\theta)}$
$\tan(\theta)=\frac{\sqrt{3}}{1}=\frac{\sqrt{3}/2}{1/2}$

1. $\text{csc }θ =\sqrt { 2 }$

$\frac{1}{\sin(\theta)}=\frac{\sqrt{2}}{1}$