ACT Math: Trigonometry 3 — Questions and Answers
Question 1: In a right triangle, the two legs measure 6 and 8. What is sin of the angle opposite the leg of length 6?
- 6/10 (Correct answer)
- 8/10
- 6/8
- 10/6
Correct answer: 6/10
The hypotenuse is 10, so sine of that angle is opposite/hypotenuse = 6/10.
Question 2: What is the exact value of tan(45°)?
- 1 (Correct answer)
- √3
- √3/3
- 0
Correct answer: 1
In a 45-45-90 triangle the legs are equal, so tan(45°) = 1.
Question 3: Using the law of sines, if a = 10, sin A = 0.5, and sin B = 0.8, what is side b?
- 16 (Correct answer)
- 12.5
- 5
- 8
Correct answer: 16
b = a · sin B / sin A = 10 · 0.8 / 0.5 = 16.
Question 4: What is the amplitude of y = 3sin(2x)?
- 3 (Correct answer)
- 2
- 6
- 1
Correct answer: 3
The amplitude is the coefficient in front of sine, which is 3.
Question 5: Which expression equals sec(θ)?
- 1/cosθ (Correct answer)
- 1/sinθ
- 1/tanθ
- cosθ/sinθ
Correct answer: 1/cosθ
Secant is the reciprocal of cosine, so sec(θ) = 1/cos(θ).
Question 6: A right triangle has a hypotenuse of 13 and one leg of 5. What is cos of the angle adjacent to the leg of length 5?
- 5/13 (Correct answer)
- 12/13
- 5/12
- 13/5
Correct answer: 5/13
Cosine is adjacent/hypotenuse = 5/13 for the angle adjacent to that leg.
Question 7: Convert π/4 radians to degrees.
- 45° (Correct answer)
- 90°
- 30°
- 60°
Correct answer: 45°
Multiply π/4 by 180/π to get 45°.
ACT Math: Trigonometry 3
In a right triangle, the two legs measure 6 and 8.
What is sin of the angle opposite the leg of length 6?