the function h is given by h(θ) = tan(2θ). which of the following statements is true? the vertical…

the function h is given by h(θ) = tan(2θ). which of the following statements is true? the vertical asymptotes of the graph of h are at θ = 1/4 + kπ/2, where k is an integer. the vertical asymptotes of the graph of h are at θ = π/2 + kπ, where k is an integer. the vertical asymptotes of the graph of h are at θ = 1/2 + kπ, where k is an integer. the vertical asymptotes of the graph of h are at θ = π/4 + kπ/2, where k is an integer.

the function h is given by h(θ) = tan(2θ). which of the following statements is true? the vertical asymptotes of the graph of h are at θ = 1/4 + kπ/2, where k is an integer. the vertical asymptotes of the graph of h are at θ = π/2 + kπ, where k is an integer. the vertical asymptotes of the graph of h are at θ = 1/2 + kπ, where k is an integer. the vertical asymptotes of the graph of h are at θ = π/4 + kπ/2, where k is an integer.

Answer

Answer:

The vertical asymptotes of the graph of (h) are at (\theta=\frac{\pi}{4}+\frac{k\pi}{2}), where (k) is an integer.

Explanation:

Step1: Recall tangent - asymptote property

The tangent function (y = \tan(x)) has vertical asymptotes at (x=\frac{\pi}{2}+n\pi), (n\in\mathbb{Z}).

Step2: Set the argument of (h(\theta)) equal to asymptote form

For (h(\theta)=\tan(2\theta)), set (2\theta=\frac{\pi}{2}+k\pi), (k\in\mathbb{Z}).

Step3: Solve for (\theta)

Divide both sides of (2\theta=\frac{\pi}{2}+k\pi) by 2. We get (\theta=\frac{\pi}{4}+\frac{k\pi}{2}), (k\in\mathbb{Z}).