write an equation that represents all asymptotes of the graph of f in the xy - plane. 1. let f(θ)=tan(2θ)+1.
write an equation that represents all asymptotes of the graph of f in the xy - plane. 1. let f(θ)=tan(2θ)+1.
Answer
Explanation:
Step1: Recall tangent - asymptote property
The tangent function $y = \tan(x)$ has asymptotes at $x=(n+\frac{1}{2})\pi$, where $n\in\mathbb{Z}$. For the function $y = \tan(2\theta)+1$, we set $2\theta=(n +\frac{1}{2})\pi$.
Step2: Solve for $\theta$
Dividing both sides of the equation $2\theta=(n+\frac{1}{2})\pi$ by 2, we get $\theta=\frac{(2n + 1)\pi}{4}$, where $n\in\mathbb{Z}$.
Answer:
$\theta=\frac{(2n + 1)\pi}{4},n\in\mathbb{Z}$