Worksheets · Algebra 2

Exact trig values worksheet for Algebra 2

The values worth knowing by heart, at the special angles and on the axes. Past the first quadrant the numbers repeat and only the signs change.

Also taught in Precalculus, at its own level and with its own examples.

Select your difficulty

Pick more than one for a sheet that mixes them.

The preview can look cramped on a phone. The PDF and printed sheet come out normal.

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Exact Trig Values

Date Period

Find each exact value or point.

  1. Find the exact sine, cosine or tangent

    sin⁡π4
  2. cos⁡60∘
  3. cos⁡π6
  4. tan⁡60∘
  5. tan⁡π6
  6. cos⁡45∘
  7. sin⁡60∘

  1. Find exact values at quadrantal angles, or write undefined

    cot⁡270∘
  2. sin⁡90∘
  3. csc⁡0∘
  4. sec⁡180∘
  5. csc⁡180∘
  6. tan⁡0∘
  7. sec⁡270∘

  1. Find the point on the unit circle

    Find (cos⁡θ,sin⁡θ) for θ=240∘.
  2. What point on the unit circle corresponds to an angle of 135∘?
  3. Write the exact coordinates where the terminal side of 330∘ crosses the unit circle.
  4. An angle of 225∘ is in standard position. Where does it cross the unit circle?
  5. Give the coordinates of the point on the unit circle at 300∘.
  6. The terminal side of 120∘ meets the unit circle at which point?

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Exact Trig ValuesAnswer keyVersion 1

Date Period

Find each exact value or point.

  1. Find the exact sine, cosine or tangent

    sin⁡π422
  2. cos⁡60∘12
  3. cos⁡π632
  4. tan⁡60∘3
  5. tan⁡π633
  6. cos⁡45∘22
  7. sin⁡60∘32

  1. Find exact values at quadrantal angles, or write undefined

    cot⁡270∘0
  2. sin⁡90∘1
  3. csc⁡0∘Undefined
  4. sec⁡180∘−1
  5. csc⁡180∘Undefined
  6. tan⁡0∘0
  7. sec⁡270∘Undefined

  1. Find the point on the unit circle

    Find (cos⁡θ,sin⁡θ) for θ=240∘.(−12,−32)
  2. What point on the unit circle corresponds to an angle of 135∘?(−22,22)
  3. Write the exact coordinates where the terminal side of 330∘ crosses the unit circle.(32,−12)
  4. An angle of 225∘ is in standard position. Where does it cross the unit circle?(−22,−22)
  5. Give the coordinates of the point on the unit circle at 300∘.(12,−32)
  6. The terminal side of 120∘ meets the unit circle at which point?(−12,32)

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

sin⁡210∘

  1. 210 is in the third quadrant, where sine is negative.
  2. Its reference angle is 30.
  3. Sine of 30 is one half.

The answer is −12.

Where students go wrong

Getting the sign right and the number wrong, or the other way round. Do them separately: the reference angle gives the number, the quadrant gives the sign.

Also called unit circle values, special angles or trig values without a calculator.

What you can put on this worksheet

Exact values of the special angles
cos⁡π4 → 22
Exact cosecant, secant and cotangent
sec⁡π3 → 2
Angles on the axes, and undefined values
csc⁡180∘ → Undefined
Coordinates on the unit circle
Give the coordinates of the point on the unit circle at 240∘. → (−12,−32)
Drawn angles, negative angles, more than one turn
Find the exact value:
csc⁡ ⁣(−11π6) → 2

Questions about these worksheets

Yes. Every exact trig values sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Algebra 2 is usually taken around 10th or 11th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the exact trig values questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are two levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 5: exact values of the special angles, exact cosecant, secant and cotangent, angles on the axes, and undefined values, coordinates on the unit circle and drawn angles, negative angles, more than one turn. Tick as many as you want and set how many of each, or let it spread them evenly.

Getting the sign right and the number wrong, or the other way round. Do them separately: the reference angle gives the number, the quadrant gives the sign.