Trigonometry, Unit Circle Coordinates to Angle (Radians) (30s)

Level 1

This math topic focuses on translating unit circle coordinates into their corresponding angles in radians. The problems provide specific coordinates located on the unit circle and ask to determine the angle measurement from the origin in terms of pi (π). Understanding and visualizing the unit circle, recognizing coordinates associated with specific radians, and applying trigonometry concepts to solve problems are practiced. Each question presents multiple-choice answers, enhancing familiarity with the unit circle's key points and angles in radian measure. This is an introductory-level topic under a broader unit on Trigonometry and the Unit Circle.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Trigonometry, Unit Circle Coordinates to Angle (Radians) (30s) Worksheet

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Trigonometry, Unit Circle Coordinates to Angle (Radians) (30s)
1
A LaTex expression showing (-1 over 2 ,-\frac{square root of 3}{2})
How many radians around the unit circle is this point?
a A LaTex expression showing 5Pi over 6 \text{ rad}
b A LaTex expression showing 4Pi over 3 \text{ rad}
2
A LaTex expression showing (-\frac{square root of 2}{2},-\frac{square root of 2}{2})
How many radians around the unit circle is this point?
a A LaTex expression showing 4Pi over 3 \text{ rad}
b A LaTex expression showing 5Pi over 4 \text{ rad}
3
A LaTex expression showing (-1,0)
How many radians around the unit circle is this point?
a A LaTex expression showing 3Pi over 2 \text{ rad}
b A LaTex expression showing Pi \text{ rad}
4
A LaTex expression showing (-1 over 2 ,\frac{square root of 3}{2})
How many radians around the unit circle is this point?
a A LaTex expression showing 3Pi over 4 \text{ rad}
b A LaTex expression showing 2Pi over 3 \text{ rad}
5
A LaTex expression showing (1 over 2 ,\frac{square root of 3}{2})
How many radians around the unit circle is this point?
a A LaTex expression showing Pi over 3 \text{ rad}
b A LaTex expression showing Pi over 4 \text{ rad}
6
A LaTex expression showing (1 over 2 ,-\frac{square root of 3}{2})
How many radians around the unit circle is this point?
a A LaTex expression showing 7Pi over 6 \text{ rad}
b A LaTex expression showing 5Pi over 3 \text{ rad}
7
A LaTex expression showing (-\frac{square root of 3}{2},-1 over 2 )
How many radians around the unit circle is this point?
a A LaTex expression showing 2Pi over 3 \text{ rad}
b A LaTex expression showing 7Pi over 6 \text{ rad}
8
A LaTex expression showing (0,-1)
How many radians around the unit circle is this point?
a A LaTex expression showing 2Pi \text{ rad}
b A LaTex expression showing 3Pi over 2 \text{ rad}