Trigonometry, Unit Circle - Angle (Radians) to Coordinates (45s)

Level 1

This math topic covers trigonometry, focusing particularly on converting angles measured in radians to coordinates on the unit circle. Problems involve key angles such as $\pi$, $\frac{\pi}{2}$, $3\frac{\pi}{2}$, $7\frac{\pi}{4}$, $\frac{\pi}{4}$, $5\frac{\pi}{4}$, and $2\pi$. Students need to identify the correct coordinates for these angles, choosing from multiple-choice answers. This topic serves as an introduction to trigonometry and the unit circle, essential for understanding relationships in trigonometric functions.

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Trigonometry, Unit Circle - Angle (Radians) to Coordinates (45s) Worksheet

Trigonometry, Unit Circle - Angle (Radians) to Coordinates (45s)

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

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

A LaTex expression showing (-1,0)

A LaTex expression showing (0,-1)

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

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

A LaTex expression showing (1,0)

A LaTex expression showing (0,1)

$A LaTex expression showing 3Pi over 2 \text{ radians}$

What are the coordinates of the point on the unit circle at 3π/2 radians?

A LaTex expression showing (0,-1)

A LaTex expression showing (-1,0)

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

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

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

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

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

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

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

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

$A LaTex expression showing 5Pi over 4 \text{ radians}$

What are the coordinates of the point on the unit circle at 5π/4 radians?

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

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

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

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

A LaTex expression showing (1,0)

A LaTex expression showing (-1,0)

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

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

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

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