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. Use the symbol toolbar at the bottom of the screen (√, π, θ, and more) to drop special characters into any answer box.
Part I — Multiple Choice
12 points
Reference angles and quadrant signs.
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Click "New problem" any time — as many as you want.
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:
Want more practice with this skill?
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.