PRE CALCULUS Pre-Calculus Trigonometry 3 — Questions and Answers
Question 1: What is the reference angle for 315°?
- 45° (Correct answer)
- 135°
- 225°
- 60°
Correct answer: 45°
315° is in Quadrant IV; its reference angle is 360° − 315° = 45°.
Question 2: Which of the following is equivalent to sin(A + B)?
- sinA cosB − cosA sinB
- sinA cosB + cosA sinB (Correct answer)
- cosA cosB − sinA sinB
- cosA cosB + sinA sinB
Correct answer: sinA cosB + cosA sinB
The sum identity for sine is sin(A + B) = sinA cosB + cosA sinB.
Question 3: What is the range of the function y = arctan(x)?
- [−π, π]
- (−π/2, π/2) (Correct answer)
- [0, π]
- (0, π)
Correct answer: (−π/2, π/2)
The range of arctan(x) is the open interval (−π/2, π/2).
Question 4: Simplify: sin²θ + cos²θ + tan²θ − sec²θ
- 2
- 0 (Correct answer)
- 1
- −1
Correct answer: 0
sin²θ + cos²θ = 1 and sec²θ − tan²θ = 1, so the expression equals 1 − 1 = 0.
Question 5: Convert 5π/6 radians to degrees.
- 120°
- 150° (Correct answer)
- 210°
- 300°
Correct answer: 150°
Multiply by 180°/π: (5π/6)(180/π) = 900/6 = 150°.
Question 6: For a right triangle with hypotenuse 13 and adjacent side 5, what is sec(θ)?
- 5/13
- 12/13
- 13/5 (Correct answer)
- 13/12
Correct answer: 13/5
sec θ = hypotenuse/adjacent = 13/5.
Question 7: What is the exact value of sin(75°) using the sum formula?
- (√6 − √2)/4
- (√6 + √2)/4 (Correct answer)
- (√2 + √3)/2
- (√3 − 1)/2
Correct answer: (√6 + √2)/4
sin(75°) = sin(45° + 30°) = sin45°cos30° + cos45°sin30° = (√2/2)(√3/2) + (√2/2)(1/2) = (√6+√2)/4.
PRE CALCULUS Pre-Calculus Trigonometry 3
What is the reference angle for 315°?