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Worksheets›Algebra 2›Trigonometric functions›Exact values on the unit circle

Exact Values on the Unit Circle Worksheets

Free printable worksheets with answer keys. Pick a level, preview the questions, then open the sheet to swap or delete any single question.

Algebra 2CCSS HSF.TF.A.3Answer key includedPDF · Print
Open in generatorStart with an easy sheet

Easy: First quadrant

  1. 1.sin 60°
  2. 2.sin 30°
  3. 3.cos 45°
  4. 4.sin 45°
  5. 5.cos 30°
  6. 6.cos 60°
Preview shows 6 of 12 questions. Every sheet is new; open it to change any question.

Worksheet variations

On the unit circle, cos θ is the x-coordinate and sin θ the y-coordinate of the point at angle θ, and tan θ = sin θ ÷ cos θ. Find the reference angle (the acute angle to the x-axis), take its value from 30°, 45° or 60°, then give it the sign of the quadrant: all positive in I, sine in II, tangent in III, cosine in IV.

Easytan 60°First quadrantMediumsin 240°All four quadrantsHardsin πRadians

How to solve it: a worked example

Find the exact value.

  1. Startcos 60°
  2. Reference angle60°
  3. Quadrant 1 decides the sign12
  4. Answer12

Common mistakes to watch for

  • Swapping the sine and cosine values of 30° and 60°.
  • Using the wrong sign for the quadrant.
  • Giving a value for tan 90°, which is undefined.

Tip: tick “Step-by-step answer key” in the generator to print each step for marking.

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FAQ

What is a reference angle?

The acute angle between the terminal side and the x-axis. The trig values of an angle equal those of its reference angle, up to sign.

How do you remember the signs in each quadrant?

"All Students Take Calculus": all positive in quadrant I, sine in II, tangent in III, cosine in IV.

Is every worksheet different?

Yes. Numbers are generated each time, and the answer key is calculated for that sheet. Swap any single question and its answer updates too.

Can I mix exact values on the unit circle with other skills?

Yes. In the generator, add more skills; each gets its own section on the sheet with its own instructions.

Is it free to print?

Yes. Generating and printing from the browser is free with no sign-up. PDF downloads need a free account.