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

Level 1

This math topic focuses on identifying angles in degrees for specific coordinates on the unit circle, mainly in 45-degree increments. Students are given coordinates in the form of expressions, and they must determine the corresponding angle on the unit circle. Each problem presents a pair of possible angles, and the student has to select the correct one. This is an introductory level practice included in a broader unit on Trigonometry and the Unit Circle. The problems incrementally explore various quadrants and axis points on the 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 (Degrees) (45s) Worksheet

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Trigonometry, Unit Circle Coordinates to Angle (Degrees) (45s)
1
A LaTex expression showing (-\frac{square root of 2}{2},-\frac{square root of 2}{2})
How many degrees around the unit circle is this point?
a
225°
b
210°
2
A LaTex expression showing (\frac{square root of 2}{2},\frac{square root of 2}{2})
How many degrees around the unit circle is this point?
a
45°
b
120°
3
A LaTex expression showing (-\frac{square root of 2}{2},\frac{square root of 2}{2})
How many degrees around the unit circle is this point?
a
120°
b
135°
4
A LaTex expression showing (1,0)
How many degrees around the unit circle is this point?
a
360°
b
270°
5
A LaTex expression showing (\frac{square root of 2}{2},-\frac{square root of 2}{2})
How many degrees around the unit circle is this point?
a
315°
b
330°
6
A LaTex expression showing (0,-1)
How many degrees around the unit circle is this point?
a
90°
b
270°
7
A LaTex expression showing (-1,0)
How many degrees around the unit circle is this point?
a
360°
b
180°
8
A LaTex expression showing (0,1)
How many degrees around the unit circle is this point?
a
270°
b
90°