PRE CALCULUS Pre-Calculus Trigonometry 4 — Questions and Answers
Question 1: What is the vertical asymptote closest to x = 0 for y = tan(x)?
- x = 0
- x = π
- x = π/2 (Correct answer)
- x = π/4
Correct answer: x = π/2
Tangent is undefined where cosine equals zero, which first occurs at x = π/2.
Question 2: Which expression equals 2sin(θ)cos(θ)?
- cos(2θ)
- sin(2θ) (Correct answer)
- tan(2θ)
- sin²(θ)
Correct answer: sin(2θ)
The double-angle identity states sin(2θ) = 2sin(θ)cos(θ).
Question 3: A unit circle has radius 1. If a point on it is at angle θ, its coordinates are:
- (sinθ, cosθ)
- (cosθ, sinθ) (Correct answer)
- (tanθ, cotθ)
- (secθ, cscθ)
Correct answer: (cosθ, sinθ)
On the unit circle, the x-coordinate is cosθ and the y-coordinate is sinθ.
Question 4: What is the solution to 2cos(x) − 1 = 0 on [0, 2π)?
- x = π/3 only
- x = π/6 and 5π/6
- x = π/3 and 5π/3 (Correct answer)
- x = π/4 and 7π/4
Correct answer: x = π/3 and 5π/3
2cos(x) = 1 → cos(x) = 1/2, which is true at x = π/3 and x = 5π/3 on [0, 2π).
Question 5: What is the cotangent of 90°?
- 1
- Undefined
- 0 (Correct answer)
- −1
Correct answer: 0
cot(90°) = cos(90°)/sin(90°) = 0/1 = 0.
Question 6: If sin(θ) = 3/5 and θ is in Quadrant II, what is tan(θ)?
- 3/4
- 4/3
- −3/4 (Correct answer)
- −4/3
Correct answer: −3/4
In Quadrant II, cosine is negative; cos θ = −4/5, so tan θ = (3/5)/(−4/5) = −3/4.
Question 7: The Law of Sines states that in any triangle:
- a/sinA = b/sinB = c/sinC (Correct answer)
- sinA/a = sinB/b ≠ sinC/c
- a² = b² + c² − 2bc cosA
- sinA + sinB + sinC = 1
Correct answer: a/sinA = b/sinB = c/sinC
The Law of Sines states that the ratio of each side to the sine of its opposite angle is constant.
PRE CALCULUS Pre-Calculus Trigonometry 4
What is the vertical asymptote closest to x = 0 for y = tan(x)?