Finding Sine and Cosine on the Unit Circle

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For 11th grade students. Find the exact value of sine and cosine for each angle by locating the quadrant and using reference angles.

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Answer key

Find cos(0 degrees) and sin(0 degrees).
cos(0) = 1, sin(0) = 0
Find cos(90 degrees) and sin(90 degrees).
cos(90) = 0, sin(90) = 1
Find cos(180 degrees) and sin(180 degrees).
cos(180) = -1, sin(180) = 0
State the quadrant and reference angle for 135 degrees.
Quadrant II; reference angle is 45 degrees.
Find the exact values of cos(135 degrees) and sin(135 degrees).
cos(135) = -sqrt(2)/2, sin(135) = sqrt(2)/2
State the quadrant and reference angle for 210 degrees.
Quadrant III; reference angle is 30 degrees.
Find the exact values of cos(210 degrees) and sin(210 degrees).
cos(210) = -sqrt(3)/2, sin(210) = -1/2
Find the exact values of cos(300 degrees) and sin(300 degrees).
cos(300) = 1/2, sin(300) = -sqrt(3)/2
Verify that sin^2(300 degrees) + cos^2(300 degrees) = 1 using your results.
(-sqrt(3)/2)^2 + (1/2)^2 = 3/4 + 1/4 = 1.