Trigonometry, Unit Circle Dimensions as Sin/Cos Ratio of Angle Degrees

Level 1

This topic focuses on applying trigonometric concepts related to the unit circle, specifically finding the sine and cosine values for given angle degrees. It covers how to determine the x and y coordinates (dimensions) of points on the unit circle at specific angles, such as 30°, 135°, 210°, 225°, and 240°. Each question provides two possible answers, all expressed as fractions, to test understanding of converting angle degrees into the corresponding sine (y dimension) and cosine (x dimension) values using the fundamental principles of trigonometry.

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

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Trigonometry, Unit Circle Dimensions as Sin/Cos Ratio of Angle Degrees Worksheet

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Trigonometry, Unit Circle Dimensions as Sin/Cos Ratio of Angle Degrees
1
An svg image showing a math problem
What is the X dimension for the unit circle point at 225°?
a A LaTex expression showing -\frac{square root of 2}{2}
b A LaTex expression showing -1 over 2
2
An svg image showing a math problem
What is the X dimension for the unit circle point at 30°?
a A LaTex expression showing \frac{square root of 3}{2}
b A LaTex expression showing -1 over 2
3
An svg image showing a math problem
What is the Y dimension for the unit circle point at 30°?
a A LaTex expression showing 1 over 2
b A LaTex expression showing \frac{square root of 3}{2}
4
An svg image showing a math problem
What is the X dimension for the unit circle point at 225°?
a A LaTex expression showing -\frac{square root of 2}{2}
b A LaTex expression showing 1 over 2
5
An svg image showing a math problem
What is the Y dimension for the unit circle point at 240°?
a A LaTex expression showing -\frac{square root of 3}{2}
b A LaTex expression showing -\frac{square root of 2}{2}
6
An svg image showing a math problem
What is the X dimension for the unit circle point at 210°?
a A LaTex expression showing -1 over 2
b A LaTex expression showing -\frac{square root of 3}{2}
7
An svg image showing a math problem
What is the X dimension for the unit circle point at 135°?
a A LaTex expression showing -\frac{square root of 2}{2}
b A LaTex expression showing -\frac{square root of 3}{2}
8
An svg image showing a math problem
What is the X dimension for the unit circle point at 210°?
a A LaTex expression showing -\frac{square root of 3}{2}
b A LaTex expression showing -\frac{square root of 2}{2}