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Trigonometry, Unit Circle Coordinates to Angle (Radians) (45s)

Level 1

This math topic focuses on trigonometry, specifically identifying angles in radians based on coordinates on the unit circle, typically at 45-degree intervals. It is part of an introductory unit on the relationship between trigonometry and the unit circle. Students are presented with specific points on the unit circle, and they are required to determine how many radians around the unit circle these points represent, selecting from multiple choices provided. This practice is crucial for mastering the placement and radian measurement of angles on 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) (45s) Worksheet

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Trigonometry, Unit Circle Coordinates to Angle (Radians) (45s)
1
A LaTex expression showing (0,-1)
How many radians around the unit circle is this point?
a A LaTex expression showing Pi over 2 \text{ rad}
b A LaTex expression showing 3Pi over 2 \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 3Pi over 4 \text{ rad}
b A LaTex expression showing Pi over 4 \text{ rad}
3
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 5Pi over 3 \text{ rad}
b A LaTex expression showing 7Pi over 4 \text{ rad}
4
A LaTex expression showing (1,0)
How many radians around the unit circle is this point?
a A LaTex expression showing Pi over 2 \text{ rad}
b A LaTex expression showing 2Pi \text{ rad}
5
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 7Pi over 6 \text{ rad}
b A LaTex expression showing 5Pi over 4 \text{ rad}
6
A LaTex expression showing (-1,0)
How many radians around the unit circle is this point?
a A LaTex expression showing Pi over 2 \text{ rad}
b A LaTex expression showing Pi \text{ rad}
7
A LaTex expression showing (0,1)
How many radians around the unit circle is this point?
a A LaTex expression showing Pi over 2 \text{ rad}
b A LaTex expression showing 3Pi over 2 \text{ rad}
8
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 3Pi over 4 \text{ rad}
b A LaTex expression showing Pi over 4 \text{ rad}