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

Level 1

This math topic focuses on applying trigonometric functions—specifically sine and cosine—to calculate dimensions of points on the unit circle at various angles measured in radians. The exercises require identifying whether sine or cosine should be used to find the X or Y coordinates based on angle measures such as π/4, π/6, 7π/6, 11π/6, 4π/3, and 3π/4. Each problem is about determining which trigonometric function correctly corresponds to a given angle's sine or cosine value, reinforcing knowledge of the unit circle and angle measures in radians.

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 and Solved Ratio of Angle Radians Worksheet

Trigonometry, Unit Circle Dimensions as Sin/Cos and Solved Ratio of A...

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What calculation gives the Y dimension for the unit circle point at π/4 radians?

a $A LaTex expression showing \cos{(Pi over 4 )}=\frac{square root of 3}{2}$

b $A LaTex expression showing \sin{(Pi over 4 )}=\frac{square root of 2}{2}$

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What calculation gives the X dimension for the unit circle point at π/6 radians?

a $A LaTex expression showing \cos{(Pi over 6 )}=\frac{square root of 3}{2}$

b $A LaTex expression showing \sin{(Pi over 6 )}=\frac{square root of 2}{2}$

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What calculation gives the Y dimension for the unit circle point at 7π/6 radians?

a $A LaTex expression showing \sin{(7Pi over 6 )}=-1 over 2$

b $A LaTex expression showing \cos{(7Pi over 6 )}=\frac{square root of 3}{2}$

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What calculation gives the Y dimension for the unit circle point at 11π/6 radians?

a $A LaTex expression showing \cos{(11Pi over 6 )}=-1 over 2$

b $A LaTex expression showing \sin{(11Pi over 6 )}=-1 over 2$

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What calculation gives the Y dimension for the unit circle point at 4π/3 radians?

a $A LaTex expression showing \sin{(4Pi over 3 )}=-\frac{square root of 3}{2}$

b $A LaTex expression showing \cos{(4Pi over 3 )}=-\frac{square root of 3}{2}$

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What calculation gives the X dimension for the unit circle point at 11π/6 radians?

a $A LaTex expression showing \sin{(11Pi over 6 )}=-1 over 2$

b $A LaTex expression showing \cos{(11Pi over 6 )}=\frac{square root of 3}{2}$

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What calculation gives the Y dimension for the unit circle point at 3π/4 radians?

a $A LaTex expression showing \cos{(3Pi over 4 )}=\frac{square root of 2}{2}$

b $A LaTex expression showing \sin{(3Pi over 4 )}=\frac{square root of 2}{2}$

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What calculation gives the Y dimension for the unit circle point at 5π/3 radians?

a $A LaTex expression showing \cos{(5Pi over 3 )}=-\frac{square root of 2}{2}$

b $A LaTex expression showing \sin{(5Pi over 3 )}=-\frac{square root of 3}{2}$