Even–Odd, Unit Circle & Radian Understanding Quiz

  • 12th Grade
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Cierra Henderson, MBA |
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Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.
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Quizzes Created: 8156 | Total Attempts: 9,586,195
| Questions: 20 | Updated: Jan 22, 2026
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1) Convert 150 degrees to radians.

Explanation

Given: 150°. Goal: convert to radians.

Step 1: Multiply by π/180 ⇒ 150·(π/180) = 5π/6.

So, the final answer is 5π/6.

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About This Quiz
Evenodd, Unit Circle & Radian Understanding Quiz - Quiz

Ready to connect even–odd patterns to the unit circle? In this quiz, you’ll use radians and coordinates on the circle to explain why sine changes sign but cosine doesn’t when angles are reflected across the origin. You’ll convert between degrees and radians, locate angles like −π/3 or π−θ, and determine... see morewhere sine, cosine, and tangent are positive or negative. By the end, you’ll see how symmetry on the unit circle reveals the beauty behind even–odd trig functions.
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2) Convert 7π/6 radians to degrees.

Explanation

Given: 7π/6. Goal: convert to degrees.

Step 1: Multiply by 180/π ⇒ (7π/6)·(180/π) = 210°.

So, the final answer is 210°.

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3) On the unit circle, the x-coordinate of a point at angle θ is:

Explanation

Given: unit-circle coordinates. Goal: identify x-coordinate.

Step 1: Point is (cos θ, sin θ).

So, the final answer is cos θ.

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4) Which identity expresses the even/odd property of cosine?

Explanation

Given: parity. Goal: property of cos.

Step 1: Cosine is even.

So, the final answer is cos(−θ)=cos θ.

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5) The angle θ = 3π/4 is on the unit circle. What are the coordinates?

Explanation

Given: θ=3π/4 (135°). Goal: (cos θ, sin θ).

Step 1: Reference angle π/4 in QII ⇒ cos negative, sin positive.

Step 2: Values: (−√2/2, √2/2).

So, the final answer is (−√2/2, √2/2).

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6) Which equals the radian measure of a full revolution?

Explanation

Given: full turn. Goal: radians.

Step 1: One revolution is 2π radians.

So, the final answer is 2π.

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7) The unit circle y-coordinate at angle θ is:

Explanation

Given: unit-circle coordinates. Goal: y-coordinate.

Step 1: Point is (cos θ, sin θ).

So, the final answer is sin θ.

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8) Which identity is true about sine as an odd function?

Explanation

Given: parity of sine. Goal: state the identity.

Step 1: Sine is odd.

So, the final answer is sin(−θ)=−sin θ.

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9) The angle 5π/6 lies in which quadrant?

Explanation

Given: 5π/6 = 150°. Goal: quadrant.

Step 1: Between π/2 and π ⇒ Quadrant II.

So, the final answer is Quadrant II.

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10) Evaluate cos(π).

Explanation

Given: cos at π. Goal: exact value.

Step 1: cos π = −1.

So, the final answer is −1.

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11) Which angle has the same terminal side as −π/3?

Explanation

Given: coterminal requirement. Goal: pick in [0, 2π).

Step 1: Add 2π: −π/3 + 2π = 5π/3.

So, the final answer is 5π/3.

Submit
12) If P(x, y) is on the unit circle, which equation must be true?

Explanation

Given: unit circle. Goal: fundamental equation.

Step 1: Definition of unit circle is x² + y² = 1.

So, the final answer is x² + y² = 1.

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13) The angle θ = 7π/4 is on the unit circle. What is sin θ?

Explanation

Given: θ=7π/4 (315°). Goal: sine value.

Step 1: Reference angle π/4 in QIV ⇒ sine negative with magnitude √2/2.

So, the final answer is −√2/2.

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14) Which is the radian measure for 135 degrees?

Explanation

Given: 135°. Goal: convert to radians.

Step 1: 135·(π/180)=3π/4.

So, the final answer is 3π/4.

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15) If cos θ = 0 and 0 ≤ θ ≤ 2π, which values of θ are possible?

Explanation

Given: where cos θ = 0. Goal: angles in [0, 2π].

Step 1: Cosine is zero on the y-axis ⇒ θ = π/2, 3π/2.

So, the final answer is π/2 or 3π/2.

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16) Using even/odd identities, simplify sin(−5π/6).

Explanation

Given: sin(−θ). Goal: simplify symbolically.

Step 1: Sine is odd ⇒ sin(−5π/6) = −sin(5π/6).

So, the final answer is −sin(5π/6).

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17) The angle θ = −π/3. What is cos θ?

Explanation

Given: θ negative. Goal: cos value.

Step 1: Cosine is even ⇒ cos(−π/3) = cos(π/3).

Step 2: cos(π/3) = 1/2.

So, the final answer is 1/2.

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18) Which statement is true about radians?

Explanation

Given: definition. Goal: choose correct statement.

Step 1: By definition, θ (radians) = s/r (arc length over radius).

So, the final answer is a radian is the ratio of arc length to radius.

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19) Evaluate sin(π − θ) in terms of sin and cos.

Explanation

Given: supplementary angle identity. Goal: expression.

Step 1: sin(π − θ) = sin θ.

So, the final answer is sin θ.

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20) Determine sin(5π/3).

Explanation

Given: 5π/3 = 300°. Goal: sine value.

Step 1: Reference angle π/3; quadrant IV ⇒ sine negative.

Step 2: |sin(π/3)| = √3/2 ⇒ result −√3/2.

So, the final answer is −√3/2.

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Cierra Henderson |MBA |
K-12 Expert
Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.
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Convert 150 degrees to radians.
Convert 7π/6 radians to degrees.
On the unit circle, the x-coordinate of a point at angle θ is:
Which identity expresses the even/odd property of cosine?
The angle θ = 3π/4 is on the unit circle. What are the coordinates?
Which equals the radian measure of a full revolution?
The unit circle y-coordinate at angle θ is:
Which identity is true about sine as an odd function?
The angle 5π/6 lies in which quadrant?
Evaluate cos(π).
Which angle has the same terminal side as −π/3?
If P(x, y) is on the unit circle, which equation must be true?
The angle θ = 7π/4 is on the unit circle. What is sin θ?
Which is the radian measure for 135 degrees?
If cos θ = 0 and 0 ≤ θ ≤ 2π, which values of θ are possible?
Using even/odd identities, simplify sin(−5π/6).
The angle θ = −π/3. What is cos θ?
Which statement is true about radians?
Evaluate sin(π − θ) in terms of sin and cos.
Determine sin(5π/3).
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