Sign in to save

Bookmark this page so you can find it later.

Sign in to save

Bookmark this page so you can find it later.
Math Grade 9-12

Math: Unit Circle and Trigonometry

Using angles, coordinates, and trig values on the unit circle

View Answer Key
Name:
Date:
Score: / 15

Using angles, coordinates, and trig values on the unit circle

Math - Grade 9-12

Instructions: Read each problem carefully. Use the unit circle relationships to find exact values when possible. Show your work in the space provided.
  1. 1
    Unit circle with radius pointing right to the point for zero degrees.

    On the unit circle, what point corresponds to an angle of 0 degrees?

  2. 2
    Unit circle with radius pointing upward to the point for ninety degrees.

    Find the coordinates on the unit circle for 90 degrees.

  3. 3
    First-quadrant unit circle radius at thirty degrees with dashed coordinate projections.

    State the exact values of sin 30 degrees and cos 30 degrees.

  4. 4
    First-quadrant unit circle radius at forty-five degrees with equal dashed projections.

    State the exact values of sin 45 degrees and cos 45 degrees.

  5. 5
    First-quadrant unit circle radius at sixty degrees with dashed component projections.

    Find tan 60 degrees using sin 60 degrees and cos 60 degrees.

  6. 6
    Unit circle point in the second quadrant corresponding to one hundred fifty degrees.

    What are the coordinates on the unit circle for 150 degrees?

  7. 7
    Unit circle point in the third quadrant just below the negative horizontal axis.

    Find the exact value of sin 210 degrees.

  8. 8
    Unit circle point in the fourth quadrant at a forty-five-degree reference angle.

    Find the exact value of cos 315 degrees.

  9. 9
    Unit circle point in the second quadrant at a forty-five-degree reference angle.

    Find the exact value of tan 135 degrees.

  10. 10

    Convert 120 degrees to radians.

  11. 11

    Convert 7pi over 6 radians to degrees.

  12. 12
    Third-quadrant unit circle radius with a reference angle shown to the horizontal axis.

    Find the reference angle for 240 degrees.

  13. 13
    First-quadrant unit circle point with dashed projections to show coordinate components.

    On the unit circle, the point for an angle theta is (square root of 3 over 2, 1/2). Find sin theta and cos theta.

  14. 14
    Unit circle point in the third quadrant with equal negative coordinate components.

    If sin theta = -square root of 2 over 2 and cos theta = -square root of 2 over 2, what angle between 0 degrees and 360 degrees is theta?

  15. 15
    Unit circle at the top point showing a vertical radius and zero horizontal component.

    Explain why tan 90 degrees is undefined using unit circle values.

LivePhysics™.com Math - Grade 9-12

Related Tools

Related Labs

Related Infographics

Related Cheat Sheets

More Math Worksheets

Addition & Subtraction with Regrouping

Grade 2-3 · 8 problems

Fractions: Parts of a Whole

Grade 4-5 · 8 problems

Word Problems: Mixed Operations

Grade 4-5 · 8 problems

Ratios & Proportions

Grade 6-8 · 8 problems
See all Math worksheets

More Grade 9-12 Worksheets

Linear Equations

Math · 8 problems

Cell Biology

Biology · 8 problems

Reading Comprehension

Language Arts · 8 problems

Historical Thinking & Evidence

Social Studies · 8 problems
See all Grade 9-12 worksheets