### Home > PC > Chapter 4 > Lesson 4.1.1 > Problem4-7

4-7.

Sketch each of the following angles onto a unit circle then find the coordinates of the angle.

1. $\theta = \frac { 5 \pi } { 3 }$

The reference angle is $\frac{\pi}{3}$. What are the cosine and sine of $\frac{\pi}{3}$? When writing your final answer, remember that this angle is in the fourth quadrant.

1. $\theta = - \frac { 5 \pi } { 4 }$

1. Draw a unit circle.
2. Divide the top and bottom halves into quarters.
3. Put a mark on the unit circle at the $5$ quarters going clockwise from ($1,0$).
4. Make a triangle with the $x$-axis.
5. Label the lengths of the sides.
6. Check for the correct signs.
7. The coordinates are ($x, y$).

What are the side lengths? Use the Pythogorean Theorem.

1. $\theta = \frac { 8 \pi } { 3 }$

$\frac{8\pi}{3}$ is the same angle as $\frac{8\pi}{3}-2\pi = \frac{2\pi}{3}$