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

Level 1

This topic focuses on advanced trigonometry skills, specifically calculating the sine and cosine values for given angle radians using the unit circle. Each question prompts learners to determine either the X or Y coordinate (cosine or sine) of a point on the unit circle corresponding to a specific angle in radians. Solutions involve recognizing and working with surd expressions, enhancing understanding of the trigonometric identities and their geometrical interpretations 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 Dimensions as Sin/Cos Ratio of Angle Radians Worksheet

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Trigonometry, Unit Circle Dimensions as Sin/Cos Ratio of Angle Radians
1
An svg image showing a math problem
What is the Y dimension for the unit circle point at 2π/3 radians?
a A LaTex expression showing \frac{square root of 3}{2}
b A LaTex expression showing \frac{square root of 2}{2}
2
An svg image showing a math problem
What is the Y dimension for the unit circle point at 11π/6 radians?
a A LaTex expression showing -1 over 2
b A LaTex expression showing -\frac{square root of 2}{2}
3
An svg image showing a math problem
What is the X dimension for the unit circle point at 5π/6 radians?
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 3π/4 radians?
a A LaTex expression showing -\frac{square root of 2}{2}
b A LaTex expression showing -\frac{square root of 3}{2}
5
An svg image showing a math problem
What is the Y dimension for the unit circle point at 5π/6 radians?
a A LaTex expression showing 1 over 2
b A LaTex expression showing \frac{square root of 3}{2}
6
An svg image showing a math problem
What is the Y dimension for the unit circle point at 5π/6 radians?
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 Y dimension for the unit circle point at π/3 radians?
a A LaTex expression showing \frac{square root of 3}{2}
b A LaTex expression showing \frac{square root of 2}{2}
8
An svg image showing a math problem
What is the Y dimension for the unit circle point at 11π/6 radians?
a A LaTex expression showing -1 over 2
b A LaTex expression showing -\frac{square root of 2}{2}