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Math · Trigonometry

Medium Trigonometry Drill

15 medium-difficulty ACT Math questions on Trigonometry. Each question is on its own page with a worked answer explanation, the underlying rule, and a quick study tip.

Medium Math Trigonometry

All 15 questions

  1. 1 Sine of a Special Angle What is sin(45°)? Medium
  2. 2 SOHCAHTOA — Sine in a Right Triangle In a right triangle, the side opposite angle θ has length 8 and the hypotenuse has length Medium
  3. 3 Pythagorean Identity What is the value of sin²(θ) + cos²(θ) for any angle θ? Medium
  4. 4 Tangent in a Right Triangle In a right triangle, the side opposite angle θ has length 3 and the side adjacent to θ has Medium
  5. 5 Sine of a Special Angle What is sin(60°)? Medium
  6. 6 SOHCAHTOA — Sine in a Right Triangle In a right triangle, the side opposite angle θ has length 3 and the hypotenuse has length Medium
  7. 7 Pythagorean Identity What is the value of sin²(θ) + cos²(θ) for any angle θ? Medium
  8. 8 Tangent in a Right Triangle In a right triangle, the side opposite angle θ has length 3 and the side adjacent to θ has Medium
  9. 9 Sine of a Special Angle What is sin(30°)? Medium
  10. 10 SOHCAHTOA — Sine in a Right Triangle In a right triangle, the side opposite angle θ has length 3 and the hypotenuse has length Medium
  11. 11 Pythagorean Identity What is the value of sin²(θ) + cos²(θ) for any angle θ? Medium
  12. 12 Tangent in a Right Triangle In a right triangle, the side opposite angle θ has length 3 and the side adjacent to θ has Medium
  13. 13 Sine of a Special Angle What is sin(45°)? Medium
  14. 14 SOHCAHTOA — Sine in a Right Triangle In a right triangle, the side opposite angle θ has length 8 and the hypotenuse has length Medium
  15. 15 Pythagorean Identity What is the value of sin²(θ) + cos²(θ) for any angle θ? Medium

How to use this drill

Open the questions one at a time. Read the prompt, decide on an answer before scrolling, then check the explanation. The point of a drill is not to "get the question right" — it's to internalize the rule so you can apply it cold under timed conditions on test day.

If you're missing more than a third of the questions in this set, drop down a difficulty tier and rebuild from there. If you're getting all of them quickly, jump up a tier and try a mixed drill across subtopics.

What "Medium" means here

Medium questions add a layer — multi-step calculation, two competing rules, or a mildly tempting wrong answer that requires careful reading. A student scoring around 26 composite should be solid here; this is also the sweet spot for most score-improvement work.

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