College Math Placement Test Trigonometry 4 — Questions and Answers
Question 1: A 20-foot ladder leans against a wall at an angle of 60° with the ground. How high up the wall does the ladder reach?
- 10√3 ft (Correct answer)
- 10 ft
- 20√3 ft
- 20/√3 ft
Correct answer: 10√3 ft
height = 20 × sin 60° = 20 × (√3/2) = 10√3 feet.
Question 2: What is the exact value of csc(30°)?
- 2 (Correct answer)
- √2
- √3
- 2√3/3
Correct answer: 2
csc 30° = 1/sin 30° = 1/(1/2) = 2.
Question 3: Which of the following is true for all angles θ?
- 1 + tan²θ = sec²θ (Correct answer)
- 1 + sin²θ = cos²θ
- sin²θ − cos²θ = 1
- tan²θ − sec²θ = 1
Correct answer: 1 + tan²θ = sec²θ
Dividing sin²θ + cos²θ = 1 by cos²θ gives tan²θ + 1 = sec²θ.
Question 4: What is the phase shift of y = sin(x − π/4)?
- π/4 to the right (Correct answer)
- π/4 to the left
- π/2 to the right
- No phase shift
Correct answer: π/4 to the right
y = sin(x − π/4) shifts the graph π/4 units to the right.
Question 5: In a right triangle, if one acute angle is θ, then the other acute angle is
- 90° − θ (Correct answer)
- 180° − θ
- θ − 90°
- 360° − θ
Correct answer: 90° − θ
The two acute angles in a right triangle sum to 90°, so the other angle is 90° − θ.
Question 6: What is the value of cos(2π)?
- 1 (Correct answer)
- -1
- 0
- √2/2
Correct answer: 1
2π corresponds to a full rotation, returning to the starting point where cos = 1.
Question 7: If tan θ = −2 and θ is in Quadrant IV, what is sec θ?
- √5 (Correct answer)
- -√5
- √5/2
- -√5/2
Correct answer: √5
sec²θ = 1 + tan²θ = 1 + 4 = 5, so sec θ = √5 (positive in QIV).
College Math Placement Test Trigonometry 4
A 20-foot ladder leans against a wall at an angle of 60° with the ground.
How high up the wall does the ladder reach?