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

Level 1

This topic focuses on trigonometry, specifically converting radians to coordinates on the unit circle. The problems require identifying the coordinates of various points given their position in radians (such as \( \frac{11\pi}{6} \), \( \frac{7\pi}{6} \), etc.). Each question provides multiple-choice options for possible coordinates, allowing for practice in understanding the unit circle's layout and function in trigonometry. This practice is geared towards beginners and is part of a broader introduction to trigonometry and 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 - Angle (Radians) to Coordinates (30s) Worksheet

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

$A LaTex expression showing 11Pi over 6 \text{ radians}$

What are the coordinates of the point on the unit circle at 11π/6 radians?

a $A LaTex expression showing (\frac{square root of 2}{2},-\frac{square root of 2}{2})$

b $A LaTex expression showing (\frac{square root of 3}{2},-1 over 2 )$

$A LaTex expression showing 7Pi over 6 \text{ radians}$

What are the coordinates of the point on the unit circle at 7π/6 radians?

a $A LaTex expression showing (-\frac{square root of 3}{2},-1 over 2 )$

b $A LaTex expression showing (-1 over 2 ,-\frac{square root of 3}{2})$

$A LaTex expression showing Pi over 6 \text{ radians}$

What are the coordinates of the point on the unit circle at π/6 radians?

a $A LaTex expression showing (-1 over 2 ,\frac{square root of 3}{2})$

b $A LaTex expression showing (\frac{square root of 3}{2},1 over 2 )$

$A LaTex expression showing 3Pi over 4 \text{ radians}$

What are the coordinates of the point on the unit circle at 3π/4 radians?

a $A LaTex expression showing (-\frac{square root of 3}{2},-1 over 2 )$

b $A LaTex expression showing (-\frac{square root of 2}{2},\frac{square root of 2}{2})$

$A LaTex expression showing 7Pi over 4 \text{ radians}$

What are the coordinates of the point on the unit circle at 7π/4 radians?

a $A LaTex expression showing (\frac{square root of 2}{2},-\frac{square root of 2}{2})$

b $A LaTex expression showing (1 over 2 ,-\frac{square root of 3}{2})$

$A LaTex expression showing 5Pi over 6 \text{ radians}$

What are the coordinates of the point on the unit circle at 5π/6 radians?

a $A LaTex expression showing (-\frac{square root of 3}{2},1 over 2 )$

b $A LaTex expression showing (-\frac{square root of 3}{2},-1 over 2 )$

$A LaTex expression showing 2Pi \text{ radians}$

What are the coordinates of the point on the unit circle at 2π radians?

A LaTex expression showing (0,1)

A LaTex expression showing (1,0)

$A LaTex expression showing Pi over 4 \text{ radians}$

What are the coordinates of the point on the unit circle at π/4 radians?

a $A LaTex expression showing (-\frac{square root of 3}{2},1 over 2 )$

b $A LaTex expression showing (\frac{square root of 2}{2},\frac{square root of 2}{2})$