PRE CALCULUS Pre-Calculus Trigonometry 4

Question 1

What is the vertical asymptote closest to x = 0 for y = tan(x)?

Accepted Answer

x = π/2

Answer

Tangent is undefined where cosine equals zero, which first occurs at x = π/2.

Question 2

Which expression equals 2sin(θ)cos(θ)?

Accepted Answer

sin(2θ)

Answer

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:

Accepted Answer

(cosθ, sinθ)

Answer

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)?

Accepted Answer

x = π/3 and 5π/3

Answer

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°?

Accepted Answer

0

Answer

cot(90°) = cos(90°)/sin(90°) = 0/1 = 0.

PRE CALCULUS Practice Test