No calculators. Leave all answers as exact values (fractions and radicals) — do not use decimal approximations. Everything below checks itself as you go. When you're done, email your results to your teacher with one click.
Part I — Multiple Choice
12 points
Reference angles and quadrant signs.
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Part II — Coordinates & Trigonometric Values
23 points
Fill in exact values. Use forms like -√3/2, 1/2, or √2/2.
7
Use the diagram to complete the table with the exact coordinates (cos θ, sin θ) for each labeled angle.
16 pts
θ
Coordinates (x, y)
θ
Coordinates (x, y)
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Click "New problem" any time — as many as you want.
Part III — Extended Response
15 points
Question 12 is self-checked; question 14 is reviewed by your teacher.
12
Find one positive angle and one negative angle that are coterminal with θ = 7π/4.
3 pts
Any angle of the form 7π/4 + 2πk works. Sample: positive 15π/4 (add 2π), negative −π/4 (subtract 2π).
14
Explain why, for any angle θ, the point (cos θ, sin θ) must lie on the unit circle x² + y² = 1. Reference a specific identity or theorem in your explanation.
4 pts
Model answer: by definition, an angle θ in standard position has its terminal side meet the unit circle at (cos θ, sin θ), and the unit circle is every point exactly 1 unit from the origin. That distance is √(cos²θ + sin²θ), and the Pythagorean identity says cos²θ + sin²θ = 1 for every θ. So the distance is always 1, meaning the point always satisfies x² + y² = 1.
Check your own explanation against these three things — your teacher will grade this one, but this tells you how you're doing:
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Click "New problem" any time — as many as you want.
You can change answers and check again as many times as you like.
Your results
0/43
Auto-graded
—
Self-checked (Q12)
4
For your teacher (Q14)
Opens an email, pre-filled with your name, your scores, and your Question 14 answer — just hit send.