PRE CALCULUS Pre-Calculus Trigonometry 2 — Questions and Answers
Question 1: What is the period of the function f(x) = sin(3x)?
- π/3
- 2π/3 (Correct answer)
- 3π
- 6π
Correct answer: 2π/3
The period of sin(bx) is 2π/b, so for b=3 the period is 2π/3.
Question 2: Which identity correctly expresses cos(2θ) in terms of sin(θ) only?
- 1 + 2sin²θ
- 1 − 2sin²θ (Correct answer)
- 2sin²θ − 1
- sin²θ − cos²θ
Correct answer: 1 − 2sin²θ
Using cos(2θ) = cos²θ − sin²θ and cos²θ = 1 − sin²θ gives 1 − 2sin²θ.
Question 3: What is the amplitude of y = −4cos(x)?
- −4
- 4 (Correct answer)
- π/4
- 2π
Correct answer: 4
Amplitude is the absolute value of the leading coefficient, so |−4| = 4.
Question 4: In which quadrant is the angle 210° located, and what is the sign of its tangent?
- Quadrant II, negative
- Quadrant III, positive (Correct answer)
- Quadrant III, negative
- Quadrant IV, positive
Correct answer: Quadrant III, positive
210° is in Quadrant III where both sine and cosine are negative, making tangent positive.
Question 5: What is the exact value of csc(π/6)?
- √3/2
- 2 (Correct answer)
- √3
- 1/2
Correct answer: 2
csc(π/6) = 1/sin(π/6) = 1/(1/2) = 2.
Question 6: The graph of y = sin(x − π/4) is the graph of y = sin(x) shifted how?
- π/4 units left
- π/4 units right (Correct answer)
- π/4 units up
- π/4 units down
Correct answer: π/4 units right
A phase shift of the form sin(x − c) shifts the graph c units to the right.
Question 7: If tan(θ) = −5/12 and θ is in Quadrant IV, what is cos(θ)?
- −12/13
- 12/13 (Correct answer)
- 5/13
- −5/13
Correct answer: 12/13
In Quadrant IV, cosine is positive; with opposite=−5 and adjacent=12, hypotenuse=13, so cos θ = 12/13.
PRE CALCULUS Pre-Calculus Trigonometry 2
What is the period of the function f(x) = sin(3x)?