### Home > PC3 > Chapter 3 > Lesson 3.1.1 > Problem3-14

3-14.

State all values of $0\leθ<2\pi$ that satisfy each of the following equations. Sketching a unit circle may help.

1. $\sin(θ)=-\frac{1}{2}$

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

1. $\cos(θ)=\frac{\sqrt{2}}{2}$

1. What special reference angle is this value related to?
2. In which quadrants is cosine positive?

1. $\tan(θ)=\sqrt{3}$

$\tan(\theta)=\frac{\sin(\theta)}{\cos(\theta)}$

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

1. $\sin(θ)=-1$

Since sine is related to the $y$-value of the coordinates of the unit circle, where on the unit circle is $y=−1$?