Free ACT Math: Trigonometry Questions and Answers 2 — Questions and Answers
Question 1: In a right triangle, the opposite side is 7 and the hypotenuse is 25. What is tan θ?
- 7/24 (Correct answer)
- 7/25
- 24/25
- 25/7
Correct answer: 7/24
First find adjacent side: adj = √(25² − 7²) = √(625 − 49) = √576 = 24. tan θ = opposite/adjacent = 7/24.
Question 2: What is the exact value of cos(60°)?
- 1/2 (Correct answer)
- √3/2
- √2/2
- √3/3
Correct answer: 1/2
From the 30-60-90 triangle: cos(60°) = adjacent/hypotenuse = 1/2. This is one of the standard values to memorize for the ACT.
Question 3: An angle measures 5π/6 radians. What is this in degrees?
- 150° (Correct answer)
- 120°
- 300°
- 210°
Correct answer: 150°
Multiply by 180°/π: (5π/6) × (180/π) = 5 × 30 = 150°.
Question 4: If cos θ = −√3/2 and 180° < θ < 270°, what is θ?
- 210° (Correct answer)
- 150°
- 240°
- 120°
Correct answer: 210°
cos θ = −√3/2 corresponds to reference angle 30°. In Quadrant III (180° < θ < 270°): θ = 180° + 30° = 210°.
Question 5: Which identity is correct?
- sin²θ + cos²θ = 1 (Correct answer)
- sin²θ − cos²θ = 1
- sin θ × cos θ = 1
- tan²θ + 1 = sin²θ
Correct answer: sin²θ + cos²θ = 1
The Pythagorean identity sin²θ + cos²θ = 1 is fundamental in trigonometry. The related identities are: tan²θ + 1 = sec²θ and cot²θ + 1 = csc²θ.
Question 6: A ladder 13 feet long leans against a wall, making a 67.4° angle with the ground. How high up the wall does the ladder reach? (Use sin 67.4° ≈ 0.923)
- Approximately 12 feet (Correct answer)
- Approximately 5 feet
- Approximately 10 feet
- Approximately 13 feet
Correct answer: Approximately 12 feet
sin 67.4° = opposite/hypotenuse = height/13. Height = 13 × 0.923 ≈ 12 feet.
Free ACT Math: Trigonometry Questions and Answers 2
In a right triangle, the opposite side is 7 and the hypotenuse is 25.
What is tan θ?