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M3-034-A07-V02
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F-TF.2
Warmup
M3-034-A07-V02
Use the unit circle to extend trig functions to all real-number radian measures.
Reduce a radian angle and evaluate exact trig values
Problem
Reduce \(θ~=~9\pi~/4\) to its unique coterminal angle in \([0,~2\pi~)\). Use the diagram to give the exact terminal point and separate sine, cosine, and tangent values.
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A
The least nonnegative coterminal angle is pi/4; the terminal point is (sqrt(2)/2, -sqrt(2)/2); sin(theta) = -sqrt(2)/2, cos(theta) = sqrt(2)/2, and tan(theta) = -1.
B
The least nonnegative coterminal angle is pi/4; the terminal point is (sqrt(2)/2, sqrt(2)/2); sin(theta) = sqrt(2)/2, cos(theta) = sqrt(2)/2, and tan(theta) = 1.
C
The least nonnegative coterminal angle is 5pi/4; the terminal point is (-sqrt(2)/2, -sqrt(2)/2); sin(theta) = -sqrt(2)/2, cos(theta) = -sqrt(2)/2, and tan(theta) = 1.
D
The least nonnegative coterminal angle is pi/4; the terminal point is (sqrt(2)/2, sqrt(2)/2); sin(theta) = sqrt(2)/2, cos(theta) = sqrt(2)/2, and tan(theta) = -1.
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Curriculum context
Standard F-TF.2
Category Functions
Domain Trigonometric Functions
Objective Use the unit circle to extend trig functions to all real-number radian measures.
Problem type Reduce a radian angle and evaluate exact trig values
