Math · Trigonometry
Sine of a Special Angle
Medium
Math
Trigonometry
Question
What is sin(30°)?
Answer choices
- 1/√3
- 1/2
- 0
- 1
- √3/2
B Correct answer: B) 1/2
Set up the problem carefully before computing. Use the unit circle: sin(30°) = ½, sin(45°) = √2/2, sin(60°) = √3/2.
Carry the arithmetic through one step at a time, double-checking signs and units. The ACT writes wrong answers to catch the most common slips, so an answer that "looks right" without verification is risky.
Plug the answer back into the original expression as a sanity check whenever the problem allows. If the substitution does not balance, you have made an arithmetic mistake earlier in the work.
The underlying rule
sin(30°) = 1/2. This is one of the special-angle values you should have memorized: 30°, 45°, and 60°.
Why each wrong answer is wrong
- A) 1/√3: A common arithmetic or sign error leads to this value; carefully redo the calculation.
- C) 0: A common arithmetic or sign error leads to this value; carefully redo the calculation.
- D) 1: A common arithmetic or sign error leads to this value; carefully redo the calculation.
- E) √3/2: A common arithmetic or sign error leads to this value; carefully redo the calculation.
Study tip
Memorize sin/cos for 0°, 30°, 45°, 60°, 90°. The ACT will test at least one of these per test, almost without fail.
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