ACT Math · Trigonometry
Graphs of sine and cosine
Amplitude, period, and phase shift.
What's tested in this subtopic
Items test the basic shape of sine and cosine graphs and the effect of changing amplitude, period, and phase shift.
Tactics that actually move your score
For y = A sin(B(x − C)) + D: A is amplitude, period is 2π/B, C is horizontal shift, D is vertical shift. 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(30°)?
- Easy What is the value of sin(30°)?
- Medium What is the value of sin(45°)?
- Medium What is the value of sin(0°)?
- Medium What is the value of sin(60°)?
- Hard What is the value of sin(60°)?
- Easy What is the value of sin(30°)?
- Easy What is the value of sin(45°)?
- Medium What is the value of sin(90°)?
- Medium What is the value of sin(60°)?
- Medium What is the value of sin(0°)?
- Hard What is the value of sin(60°)?
- 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.