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Trigonometry, Unit Circle - Picture (Radians) to Coordinates (30s)

Level 1

This math topic focuses on identifying coordinates of specific points on the unit circle, given their positions in radians. It helps students strengthen their understanding of trigonometry within the context of the unit circle, including converting angles in radians to coordinate points. The problems range from identifying the coordinates at standard angles like \(3\pi/2\) to less common ones such as \(5\pi/3\) and \(5\pi/4\), using multiple-choice formats with visual aids and LaTeX-rendered expressions for clear representation of square roots and fractions.

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

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Trigonometry, Unit Circle - Picture (Radians) to Coordinates (30s) Worksheet

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Trigonometry, Unit Circle - Picture (Radians) to Coordinates (30s)
1
An svg image showing a math problem
What are the coordinates of the unit circle point at 3π/2 radians
a A LaTex expression showing (0,-1)
b A LaTex expression showing (1,0)
2
An svg image showing a math problem
What are the coordinates of the unit circle point at 5π/3 radians
a A LaTex expression showing (-\frac{square root of 2}{2},-\frac{square root of 2}{2})
b A LaTex expression showing (1 over 2 ,-\frac{square root of 3}{2})
3
An svg image showing a math problem
What are the coordinates of the unit circle point at π/4 radians
a A LaTex expression showing (1 over 2 ,\frac{square root of 3}{2})
b A LaTex expression showing (\frac{square root of 2}{2},\frac{square root of 2}{2})
4
An svg image showing a math problem
What are the coordinates of the unit circle point at 5π/4 radians
a A LaTex expression showing (-\frac{square root of 3}{2},1 over 2 )
b A LaTex expression showing (-\frac{square root of 2}{2},-\frac{square root of 2}{2})
5
An svg image showing a math problem
What are the coordinates of the unit circle point at π/4 radians
a A LaTex expression showing (-\frac{square root of 2}{2},\frac{square root of 2}{2})
b A LaTex expression showing (\frac{square root of 2}{2},\frac{square root of 2}{2})
6
An svg image showing a math problem
What are the coordinates of the unit circle point at 5π/4 radians
a A LaTex expression showing (1 over 2 ,-\frac{square root of 3}{2})
b A LaTex expression showing (-\frac{square root of 2}{2},-\frac{square root of 2}{2})
7
An svg image showing a math problem
What are the coordinates of the unit circle point at π/3 radians
a A LaTex expression showing (-1 over 2 ,\frac{square root of 3}{2})
b A LaTex expression showing (1 over 2 ,\frac{square root of 3}{2})
8
An svg image showing a math problem
What are the coordinates of the unit circle point at π/2 radians
a A LaTex expression showing (-1,0)
b A LaTex expression showing (0,1)