Worksheets · Algebra 2

Trig ratios of general angles worksheet

Once the angle leaves the first quadrant the ratios are the same numbers with signs attached, and the point on the terminal side tells you both at once.

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Name

Trig Ratios of General Angles

Date Period

Find each ratio.

  1. The point (24,−7) is on the terminal side of θ. Find tan⁡θ
  2. The point (−5,−12) is on the terminal side of θ. Find tan⁡θ
  3. The point (8,15) is on the terminal side of θ. Find sin⁡θ
  4. The point (3,4) is on the terminal side of θ. Find tan⁡θ
  5. The point (5,12) is on the terminal side of θ. Find cos⁡θ
  6. The point (24,7) is on the terminal side of θ. Find cos⁡θ
  7. The point (7,−24) is on the terminal side of θ. Find tan⁡θ
  8. The point (20,−21) is on the terminal side of θ. Find sin⁡θ
  9. The point (15,8) is on the terminal side of θ. Find cos⁡θ
  10. The point (4,3) is on the terminal side of θ. Find tan⁡θ
  11. The point (−5,−12) is on the terminal side of θ. Find sin⁡θ
  12. The point (−24,−7) is on the terminal side of θ. Find tan⁡θ
  13. The point (−20,21) is on the terminal side of θ. Find tan⁡θ
  14. The point (−12,−5) is on the terminal side of θ. Find tan⁡θ
  15. The point (−3,−4) is on the terminal side of θ. Find tan⁡θ
  16. The point (3,4) is on the terminal side of θ. Find sin⁡θ
  17. The point (−7,−24) is on the terminal side of θ. Find tan⁡θ
  18. The point (20,21) is on the terminal side of θ. Find tan⁡θ
  19. The point (12,−5) is on the terminal side of θ. Find sin⁡θ
  20. The point (24,−7) is on the terminal side of θ. Find sin⁡θ

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

Sigma Prep · sigmaprep.io/worksheets

Name

Trig Ratios of General AnglesAnswer keyVersion 1

Date Period

Find each ratio.

  1. The point (24,−7) is on the terminal side of θ. Find tan⁡θ−724
  2. The point (−5,−12) is on the terminal side of θ. Find tan⁡θ125
  3. The point (8,15) is on the terminal side of θ. Find sin⁡θ1517
  4. The point (3,4) is on the terminal side of θ. Find tan⁡θ43
  5. The point (5,12) is on the terminal side of θ. Find cos⁡θ513
  6. The point (24,7) is on the terminal side of θ. Find cos⁡θ2425
  7. The point (7,−24) is on the terminal side of θ. Find tan⁡θ−247
  8. The point (20,−21) is on the terminal side of θ. Find sin⁡θ−2129
  9. The point (15,8) is on the terminal side of θ. Find cos⁡θ1517
  10. The point (4,3) is on the terminal side of θ. Find tan⁡θ34
  11. The point (−5,−12) is on the terminal side of θ. Find sin⁡θ−1213
  12. The point (−24,−7) is on the terminal side of θ. Find tan⁡θ724
  13. The point (−20,21) is on the terminal side of θ. Find tan⁡θ−2120
  14. The point (−12,−5) is on the terminal side of θ. Find tan⁡θ512
  15. The point (−3,−4) is on the terminal side of θ. Find tan⁡θ43
  16. The point (3,4) is on the terminal side of θ. Find sin⁡θ45
  17. The point (−7,−24) is on the terminal side of θ. Find tan⁡θ247
  18. The point (20,21) is on the terminal side of θ. Find tan⁡θ2120
  19. The point (12,−5) is on the terminal side of θ. Find sin⁡θ−513
  20. The point (24,−7) is on the terminal side of θ. Find sin⁡θ−725

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

How to do these

The point (−3,4) is on the terminal side of θ. Find sin⁡θ

  1. The distance to the origin is 5.
  2. Sine is y over r.

The answer is 45.

Where students go wrong

Dropping the signs. The radius is always positive, but x and y carry their own signs, so a point in the second quadrant gives a positive sine and a negative cosine. Sketching the point takes five seconds and settles it.

Also called trig functions of any angle, terminal side or ASTC.

Questions about these worksheets

Yes. Every trig ratios of general angles 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 trig ratios of general angles 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 three 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.

Dropping the signs. The radius is always positive, but x and y carry their own signs, so a point in the second quadrant gives a positive sine and a negative cosine. Sketching the point takes five seconds and settles it.