Unit Circle Sine and Cosine Practice Quiz (Pre-Calculus)

📚 Topic Summary

The unit circle is a circle with a radius of 1 centered at the origin (0,0) in the coordinate plane. It's a powerful tool for understanding trigonometric functions like sine and cosine. For any angle $\theta$, the point where the terminal side of the angle intersects the unit circle has coordinates $(\cos(\theta), \sin(\theta))$. This means the x-coordinate is the cosine of the angle, and the y-coordinate is the sine of the angle.

This quiz will help you practice finding sine and cosine values for common angles on the unit circle and understanding the related vocabulary. Good luck!

🧠 Part A: Vocabulary

Match the term with its definition:

1. Term: Radian
2. Term: Unit Circle
3. Term: Sine
4. Term: Cosine
5. Term: Angle

1. Definition: A measure of rotation between two rays.
2. Definition: The x-coordinate of a point on the unit circle.
3. Definition: A circle with a radius of 1 centered at the origin.
4. Definition: The y-coordinate of a point on the unit circle.
5. Definition: A unit of angular measure equal to the angle subtended at the center of a circle by an arc equal in length to the radius.

✏️ Part B: Fill in the Blanks

The unit circle has a radius of _____. For an angle $\theta$, the coordinates of the point where the terminal side of the angle intersects the unit circle are ($_____, _____$). The sine of an angle is the _____ -coordinate, and the cosine of an angle is the _____ -coordinate. Therefore, $\sin(0) = $____ and $\cos(0) = $____.

🤔 Part C: Critical Thinking

Explain how you can use the unit circle to find the sine and cosine of angles greater than $2\pi$ or less than $0$. Give an example.