ACT Math · Trigonometry
Basic trig identities
sin²θ + cos²θ = 1 and tan = sin/cos.
What's tested in this subtopic
Items use the Pythagorean identity sin²θ + cos²θ = 1 to find one trig value given another, or use tan θ = sin θ / cos θ.
Tactics that actually move your score
When given sin θ and asked for cos θ (or vice versa), use the Pythagorean identity. Watch for sign based on the quadrant if specified. The single biggest leverage point on most subtopics isn't learning more math — it's recognizing the test's preferred surface forms quickly enough that you don't burn 30 seconds re-reading the question. The first time you see a particular phrasing it might take you a full minute. The tenth time you see it, you should be reaching for your method before you've finished the sentence. Repetition is what builds that recognition. Fifteen problems in a row of the same shape is more useful than fifty mixed.
Practice questions (14)
- Easy What is the value of sin(90°)?
- Easy What is the value of sin(60°)?
- Medium What is the value of sin(45°)?
- Medium What is the value of sin(30°)?
- Medium What is the value of sin(60°)?
- Hard What is the value of sin(0°)?
- Easy What is the value of sin(0°)?
- Easy What is the value of sin(45°)?
- Medium What is the value of sin(60°)?
- Medium What is the value of sin(90°)?
- Medium What is the value of sin(45°)?
- Hard What is the value of sin(30°)?
- Easy What is the value of sin(45°)?
- Easy What is the value of sin(60°)?
How to drill
Work through the questions above untimed. After each one, read the worked solution from start to finish — even when you got it right. Note which solution method you used, and which method we used; if they differ, ask yourself which would have been faster on test day. Speed in ACT math comes from shortening your method-selection step, not from doing arithmetic faster. Most fast students are doing the same arithmetic everyone else is — they're just spending less time deciding what to do.
Once you can clear the easy and medium items in this subtopic at 90% accuracy, attempt a timed mini-set of ten hard items at 75 seconds each. If you finish in time and score 7+ correct, you've effectively mastered the subtopic for test purposes and can move on.