ACT · Trigonometry · Basic trig identities
Question act-q-00543
Medium Multiple choice No calculator
The question
What is the value of sin(45°)?
- √2/2
- ½
- 1
- √3/2
Show answer & worked solution
Answer: √2/2
Worked solution. Recall the unit circle: sin(45°) = √2/2.
Why each wrong choice is wrong. The classic distractor swaps sine and cosine values for the same angle. Drilling the unit circle eliminates this entirely.
Test-day tactic. Memorize sine and cosine at 0°, 30°, 45°, 60°, and 90°. The values are short and they appear constantly.
About this question type
Items use the Pythagorean identity sin²θ + cos²θ = 1 to find one trig value given another, or use tan θ = sin θ / cos θ.
You will see a question shaped like this one on roughly every other official ACT form, typically at a moderate position in the section — solidly within the range that separates a 600-band student from a 700-band student. Treat any miss in this subtopic as a signal to drill the subtopic page before you do another full practice test.