ACT Math · 7% of the test
Trigonometry
Trigonometry covers right-triangle trigonometry, the unit circle, basic trig identities, and graphs of trig functions.
What's actually tested
Although the smallest content category, trigonometry items are concentrated at the back of the math section and are disproportionately Hard difficulty. Mastering them is high-leverage for students aiming for a 30+.
Subtopics
Click any subtopic to see filed practice questions, worked solutions, and a short tactical guide.
Right triangle trigonometry
Sine, cosine, and tangent of right triangle angles.
The unit circle and special angles
Sine and cosine values at 0°, 30°, 45°, 60°, and 90°.
Basic trig identities
sin²θ + cos²θ = 1 and tan = sin/cos.
Graphs of sine and cosine
Amplitude, period, and phase shift.
Sample practice questions in this topic
- Easy Right triangle trigonometry In a right triangle, the two legs have lengths 3 and 4. What is the length of the hypotenuse?
- Easy Right triangle trigonometry What is the value of sin(45°)?
- Medium Right triangle trigonometry In a right triangle, the two legs have lengths 5 and 12. What is the length of the hypotenuse?
- Medium Right triangle trigonometry What is the value of sin(45°)?
- Medium Right triangle trigonometry In a right triangle, the two legs have lengths 9 and 12. What is the length of the hypotenuse?
- Hard Right triangle trigonometry What is the value of sin(60°)?
- Easy Right triangle trigonometry In a right triangle, the two legs have lengths 7 and 24. What is the length of the hypotenuse?
- Easy Right triangle trigonometry What is the value of sin(0°)?
- Medium Right triangle trigonometry In a right triangle, the two legs have lengths 7 and 24. What is the length of the hypotenuse?
- Medium Right triangle trigonometry What is the value of sin(0°)?
- Medium Right triangle trigonometry In a right triangle, the two legs have lengths 6 and 8. What is the length of the hypotenuse?
- Hard Right triangle trigonometry What is the value of sin(45°)?
See all 56 questions in Trigonometry →
How students lose points here
Using the wrong trig ratio (sine instead of cosine), forgetting the difference between degrees and radians, and reading the unit circle at the wrong reference angle. The good news: nearly every common mistake on this topic comes from one of three or four recurring patterns. Spend an hour reviewing those patterns and your accuracy on this topic typically jumps two or three percentage points immediately, which on a balanced test is worth ten to twenty scaled score points depending on your band.
How to study this topic
Memorize SOH-CAH-TOA, the special right triangle ratios, the unit circle key values, and the Pythagorean identity. That's the entire syllabus. A reasonable session looks like fifteen practice items, untimed, with you reading the worked solution after every one — even the questions you got right, because being right by accident teaches nothing. After two or three such sessions, attempt a timed mini-set of ten items. If your accuracy stays above 80%, move on. If it doesn't, drill the lowest-accuracy subtopic for another session before you push forward.