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

Level 1

This math topic centers on applying trigonometry fundamentals in the context of the unit circle, specifically converting specific angles measured in radians to their corresponding cosine and sine coordinates. It involves determining the coordinates for angles such as \( \frac{\pi}{4} \), \( \frac{3\pi}{4} \), \( \frac{7\pi}{4} \), \( \frac{\pi}{2} \), \( \frac{3\pi}{2} \), \( \frac{5\pi}{4} \), and \( \pi \). Each question requires identifying the correct pair of cosine and sine values from given options, reinforcing advanced understanding of the unit circle in trigonometry.

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

more

Worksheet ViewUnit

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

Trigonometry, Unit Circle - Angle (Radians) to Cos/Sin Coordinates (4...

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

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

a $A LaTex expression showing (\cos{(7Pi over 4 )},\sin{(7Pi over 4 )})$

b $A LaTex expression showing (\sin{(7Pi over 4 )},\cos{(7Pi over 4 )})$

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

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

a $A LaTex expression showing (\cos{(3Pi over 4 )},\sin{(3Pi over 4 )})$

b $A LaTex expression showing (\sin{(3Pi over 4 )},\cos{(3Pi over 4 )})$

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

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

a $A LaTex expression showing (\sin{(Pi over 4 )},\cos{(Pi over 4 )})$

b $A LaTex expression showing (\cos{(Pi over 4 )},\sin{(Pi over 4 )})$

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

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

a $A LaTex expression showing (\sin{(Pi over 2 )},\cos{(Pi over 2 )})$

b $A LaTex expression showing (\cos{(Pi over 2 )},\sin{(Pi over 2 )})$

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

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

a $A LaTex expression showing (\cos{(3Pi over 2 )},\sin{(3Pi over 2 )})$

b $A LaTex expression showing (\sin{(3Pi over 2 )},\cos{(3Pi over 2 )})$

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

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

a $A LaTex expression showing (\sin{(5Pi over 4 )},\cos{(5Pi over 4 )})$

b $A LaTex expression showing (\cos{(5Pi over 4 )},\sin{(5Pi over 4 )})$

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

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

a $A LaTex expression showing (\cos{(Pi )},\sin{(Pi )})$

b $A LaTex expression showing (\sin{(Pi )},\cos{(Pi )})$

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

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

a $A LaTex expression showing (\sin{(2Pi )},\cos{(2Pi )})$

b $A LaTex expression showing (\cos{(2Pi )},\sin{(2Pi )})$