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

Level 1

This math topic focuses on understanding trigonometric functions using the unit circle, specifically calculating the sine and cosine values of given angles in radians. The main skills practiced include identifying the x and y dimensions (cosine and sine values, respectively) of points on the unit circle at various specific angles such as 2π/3, 4π/3, π/4, 7π/4, π/6, and 5π/3. The problems help solidify one's understanding of the unit circle in the context of trigonometry fundamentals at an advanced level.

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 of Angle Radians Worksheet

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Trigonometry, Unit Circle Dimensions as Sin/Cos of Angle Radians
1
An svg image showing a math problem
What is the X dimension for the unit circle point at 2π/3 radians?
a A LaTex expression showing \cos{(2Pi over 3 )}
b A LaTex expression showing \sin{(2Pi over 3 )}
2
An svg image showing a math problem
What is the X dimension for the unit circle point at 4π/3 radians?
a A LaTex expression showing \cos{(4Pi over 3 )}
b A LaTex expression showing \sin{(4Pi over 3 )}
3
An svg image showing a math problem
What is the X dimension for the unit circle point at π/4 radians?
a A LaTex expression showing \cos{(Pi over 4 )}
b A LaTex expression showing \sin{(Pi over 4 )}
4
An svg image showing a math problem
What is the X dimension for the unit circle point at 7π/4 radians?
a A LaTex expression showing \sin{(7Pi over 4 )}
b A LaTex expression showing \cos{(7Pi over 4 )}
5
An svg image showing a math problem
What is the X dimension for the unit circle point at π/4 radians?
a A LaTex expression showing \cos{(Pi over 4 )}
b A LaTex expression showing \sin{(Pi over 4 )}
6
An svg image showing a math problem
What is the X dimension for the unit circle point at 5π/3 radians?
a A LaTex expression showing \sin{(5Pi over 3 )}
b A LaTex expression showing \cos{(5Pi over 3 )}
7
An svg image showing a math problem
What is the Y dimension for the unit circle point at π/6 radians?
a A LaTex expression showing \sin{(Pi over 6 )}
b A LaTex expression showing \cos{(Pi over 6 )}
8
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 \cos{(3Pi over 4 )}
b A LaTex expression showing \sin{(3Pi over 4 )}