Reference Angles & the Unit Circle

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  • 0:01 The Unit Circle
  • 0:47 Reference Angles
  • 1:58 How to Use the Unit Circle
  • 2:56 Example
  • 3:24 Lesson Summary
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Watch this video lesson to learn how you can use the unit circle and its reference angles to help you solve trigonometry problems. Learn how to find your answers from the unit circle.

The Unit Circle

Meet the unit circle.

reference angles

The unit circle is simply a circle with a radius of 1. But, add in a few angles, and you have a very useful tool to help you easily find answers to trigonometry problems. This unit circle that we are looking at has the angles in degrees. We can also redo this unit circle so that the degrees are in radians. Remember, degrees and radians are two different ways of writing how big your angle is.

reference angles

The pink numbers that you see in parentheses show you the answers to the cosine and sine functions for the angles on the unit circle. As you can see, these answers are the same for both the unit circle in degrees and the unit circle in radians.

Reference Angles

Notice that there are a select number of angles written on this unit circle. The degrees unit circle and the radians unit circle have the same angles on them. We call these angles the reference angles. This is because only these angles have easy answers that are not a long decimal number. Look at all answers, and you won't see a long decimal number. You see easy numbers, such as 0 and 1, or easy fractions, such as 1/2. Look at the degrees unit circle, and you will see that the reference angles are 0, 30, 45, 60, 90, 120, 135, 150, 180, 210, 225, 240, 270, 300, 315, and 330 degrees. The equivalent angles in radians are 0, pi/6, pi/4, pi/3, pi/2, 2pi/3, 3pi/4, 5pi/6, pi, 7pi/6, 5pi/4, 4pi/3, 3pi/2, 5pi/3, 7pi/4, and 11pi/6.

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