Grade 12 Unit Circle Mastery Worksheet
A comprehensive worksheet for Grade 12 students to practice and master concepts related to the unit circle in trigonometry.
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Grade 12 Unit Circle Mastery Worksheet
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Read each question carefully and provide the best answer. Show all your work for full credit. You may refer to a unit circle diagram if needed.
1. What is the definition of the unit circle in trigonometry?
2. Explain the relationship between the coordinates (x, y) on the unit circle and the trigonometric functions sine and cosine for an angle θ.
Use the unit circle diagram below to answer the following questions.
3. What are the coordinates on the unit circle for an angle of 270°?
(0, 1)
(1, 0)
(0, -1)
(-1, 0)
4. If the terminal side of an angle θ in standard position passes through the point (-√3/2, 1/2) on the unit circle, what is the value of sin(θ)?
-√3/2
1/2
√3/2
-1/2
5. The radian measure of an angle is the ratio of the arc length to the .
6. An angle of 3π/2 radians is equivalent to degrees.
7. The tangent of an angle θ on the unit circle is defined as the ratio of to .
8. Find the exact values of sin(θ), cos(θ), and tan(θ) for an angle θ = 5π/6 radians. Show your work.
9. If cos(θ) = -1/2 and θ is in Quadrant III, find the exact value of sin(θ).
10. The range of the sine function is [-1, 1].
True
False
11. The terminal side of 450° lies on the positive y-axis.
True
False