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The Unit Circle

The Unit Circle. ©2002 by R. Villar All Rights Reserved. sin. The Unit Circle. 1. cos. The x-axis corresponds to the cosine function, and the y-axis corresponds to the sine function. The angles are measured from the positive x-axis (standard position) counterclockwise.

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The Unit Circle

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  1. The Unit Circle ©2002 by R. Villar All Rights Reserved

  2. sin The Unit Circle 1 cos The x-axis corresponds to the cosine function, and the y-axis corresponds to the sine function. The angles are measured from the positive x-axis (standard position) counterclockwise. In order to create the unit circle, we must use the special right triangles below: One of the most useful tools in trigonometry is the unit circle. It is a circle, with radius 1 unit, that is on the x-y coordinate plane. 45º 1 60º 1 30º 45º 30º -60º -90º 45º -45º -90º The hypotenuse for each triangle is 1 unit.

  3. You first need to find the lengths of the other sides of each right triangle... 45º 1 60º 1 30º 45º

  4. Now, use the corresponding triangle to find the coordinates on the unit circle... (0, 1) sin What are the coordinates of this point? This cooresponds to (cos 30,sin 30) (Use your 30-60-90 triangle) (cos 30, sin 30) 30º cos (1, 0) (–1, 0) (0, –1)

  5. Now, use the corresponding triangle to find the coordinates on the unit circle... (0, 1) sin What are the coordinates of this point? (Use your 45-45-90 triangle) (cos45, sin 45) (cos 30, sin 30) 45º cos (1, 0) (–1, 0) (0, –1)

  6. You can use your special right triangles to find any of the points on the unit circle... (0, 1) sin (cos45, sin 45) (cos 30, sin 30) cos (1, 0) (–1, 0) (Use your 30-60-90 triangle) What are the coordinates of this point? (0, –1) (cos 270, sin 270)

  7. Use this same technique to complete the unit circle on your own. (0, 1) sin (cos45, sin 45) (cos 30, sin 30) cos (1, 0) (–1, 0) (0, –1) (cos 270, sin 270)

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