PRE CALCULUS Pre-Calculus Trigonometry 5 — Questions and Answers
Question 1: What is the inverse sine (arcsin) of −1?
- π
- −π/2 (Correct answer)
- π/2
- 3π/2
Correct answer: −π/2
arcsin(−1) = −π/2 because sin(−π/2) = −1 and −π/2 is in the restricted range [−π/2, π/2].
Question 2: In a triangle with sides a = 7, b = 10, and included angle C = 60°, what is the value of c²?
- 79 (Correct answer)
- 219
- 149
- 51
Correct answer: 79
By the Law of Cosines: c² = 7² + 10² − 2(7)(10)cos60° = 49 + 100 − 70 = 79.
Question 3: What is the phase shift of y = cos(2x + π)?
- π to the right
- π/2 to the left (Correct answer)
- π to the left
- π/4 to the right
Correct answer: π/2 to the left
Rewrite as cos(2(x + π/2)); the phase shift is π/2 units to the left.
Question 4: Which of the following angles is co-terminal with −45°?
- 225°
- 270°
- 315° (Correct answer)
- 135°
Correct answer: 315°
Adding 360° to −45° gives 315°, which is co-terminal.
Question 5: What does the identity 1 + cot²θ = csc²θ follow from?
- Dividing sin²θ + cos²θ = 1 by sin²θ (Correct answer)
- Dividing sin²θ + cos²θ = 1 by cos²θ
- The sum formula for sine
- The double-angle formula
Correct answer: Dividing sin²θ + cos²θ = 1 by sin²θ
Dividing every term of sin²θ + cos²θ = 1 by sin²θ yields 1 + cot²θ = csc²θ.
Question 6: An angle of 5π/3 radians is equivalent to how many degrees?
- 240°
- 270°
- 300° (Correct answer)
- 330°
Correct answer: 300°
(5π/3)(180/π) = 900/3 = 300°.
Question 7: The area of a triangle with sides b = 8, c = 11, and included angle A = 30° is:
- 44
- 22 (Correct answer)
- 88
- 11√3
Correct answer: 22
Area = (1/2)bc sinA = (1/2)(8)(11)sin30° = 44 × 0.5 = 22.
PRE CALCULUS Pre-Calculus Trigonometry 5
What is the inverse sine (arcsin) of −1?