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

Level 1

This topic practices advanced trigonometry skills involving the unit circle. It focuses on calculating the sine and cosine values for various angles, specifically how these functions determine the X and Y dimensions (coordinates) of points on the unit circle. The problems provide specific angle measures such as 240°, 300°, 150°, and 225°, and ask for the corresponding sine or cosine value, reflecting an understanding of how trigonometric ratios correspond to coordinates on the unit circle. Each question is centered around interpreting and calculating these trigonometric values for given angle degrees.

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 Degrees Worksheet

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

What calculation gives the Y dimension for the unit circle point at 240°?

a $A LaTex expression showing \cos{(240 to the power of circle )}=-\frac{square root of 2}{2}$

b $A LaTex expression showing \sin{(240 to the power of circle )}=-\frac{square root of 3}{2}$

What calculation gives the X dimension for the unit circle point at 300°?

a $A LaTex expression showing \cos{(300 to the power of circle )}=1 over 2$

b $A LaTex expression showing \sin{(300 to the power of circle )}=\frac{square root of 2}{2}$

What calculation gives the Y dimension for the unit circle point at 150°?

a $A LaTex expression showing \cos{(150 to the power of circle )}=-\frac{square root of 2}{2}$

b $A LaTex expression showing \sin{(150 to the power of circle )}=1 over 2$

What calculation gives the Y dimension for the unit circle point at 300°?

a $A LaTex expression showing \cos{(300 to the power of circle )}=-\frac{square root of 2}{2}$

b $A LaTex expression showing \sin{(300 to the power of circle )}=-\frac{square root of 3}{2}$

What calculation gives the X dimension for the unit circle point at 300°?

a $A LaTex expression showing \sin{(300 to the power of circle )}=-1 over 2$

b $A LaTex expression showing \cos{(300 to the power of circle )}=1 over 2$

What calculation gives the X dimension for the unit circle point at 225°?

a $A LaTex expression showing \cos{(225 to the power of circle )}=-\frac{square root of 2}{2}$

b $A LaTex expression showing \sin{(225 to the power of circle )}=-\frac{square root of 3}{2}$

What calculation gives the X dimension for the unit circle point at 240°?

a $A LaTex expression showing \sin{(240 to the power of circle )}=-\frac{square root of 3}{2}$

b $A LaTex expression showing \cos{(240 to the power of circle )}=-1 over 2$

What calculation gives the Y dimension for the unit circle point at 240°?

a $A LaTex expression showing \sin{(240 to the power of circle )}=-\frac{square root of 3}{2}$

b $A LaTex expression showing \cos{(240 to the power of circle )}=1 over 2$