PRE CALCULUS Trigonometry 5 — Questions and Answers
Question 1: The area of a triangle with sides a = 7, b = 9, and included angle C = 60° is:
- 63√3/4 (Correct answer)
- 63/4
- 63√2/4
- 9√3/2
Correct answer: 63√3/4
Area = (1/2)ab·sin(C) = (1/2)(7)(9)·sin(60°) = (63/2)(√3/2) = 63√3/4.
Question 2: Which of the following represents a half-angle formula for cos(θ/2)?
- ±√((1 + cosθ)/2) (Correct answer)
- ±√((1 - cosθ)/2)
- ±√((cosθ - 1)/2)
- ±√((2cosθ)/1)
Correct answer: ±√((1 + cosθ)/2)
The half-angle identity for cosine is cos(θ/2) = ±√((1 + cosθ)/2).
Question 3: For y = -2cos(x) + 1, what is the vertical shift and reflection?
- Shifted up 1 unit and reflected over the x-axis (Correct answer)
- Shifted down 1 unit and reflected over the y-axis
- Shifted up 2 units with no reflection
- Shifted up 1 unit with no reflection
Correct answer: Shifted up 1 unit and reflected over the x-axis
The coefficient -2 reflects the graph over the x-axis, and the +1 shifts it up 1 unit.
Question 4: In which quadrant is an angle θ if sin(θ) > 0 and tan(θ) < 0?
- Quadrant II (Correct answer)
- Quadrant I
- Quadrant III
- Quadrant IV
Correct answer: Quadrant II
Sine is positive in Q1 and Q2; tangent is negative in Q2 and Q4; the overlap is Quadrant II.
Question 5: What is the simplified form of sin(x)·cot(x)?
- cos(x) (Correct answer)
- tan(x)
- sec(x)
- 1
Correct answer: cos(x)
sin(x)·cot(x) = sin(x)·(cos(x)/sin(x)) = cos(x).
Question 6: Using the sum-to-product formula, cos(A) + cos(B) equals:
- 2cos((A+B)/2)cos((A-B)/2) (Correct answer)
- 2sin((A+B)/2)sin((A-B)/2)
- 2cos((A-B)/2)sin((A+B)/2)
- cos((A+B)/2)cos((A-B)/2)
Correct answer: 2cos((A+B)/2)cos((A-B)/2)
The sum-to-product identity is cos(A) + cos(B) = 2cos((A+B)/2)cos((A-B)/2).
Question 7: A Ferris wheel with radius 40 ft rotates so that the height of a rider is h(t) = 40sin(πt/15) + 45. What is the maximum height?
- 85 ft (Correct answer)
- 45 ft
- 40 ft
- 5 ft
Correct answer: 85 ft
The maximum occurs when sin(πt/15) = 1, giving h = 40(1) + 45 = 85 ft.
PRE CALCULUS Trigonometry 5
The area of a triangle with sides a = 7, b = 9, and included angle C = 60° is: