### Home > PC3 > Chapter 2 > Lesson 2.2.1 > Problem2-48

2-48.

Sketch each of the following angles in a unit circle. Then state the coordinates of the corresponding point on the unit circle.

1. $θ=\frac{5\pi}{3}$

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. $θ=-\frac{5\pi}{4}$

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. $θ=\frac{8\pi}{3}$

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