Question

SOMEONE PLEASE HELP ME!!!

What are the x-intercepts of the graph of the function y=6tan(x/2)-3?

Answer 1

The closest I can get you is either (0.9273+2pi, 0) or (0.9273+2npi, 0).

Answer 2

$\text{Consider the function}\\ \\ y=6\tan(x/2)-3\\ \\ \text{to find the x-intercepts of the graph of the function, we put y=0.}\\ \text{so we get}\\ \\ 6\tan(x/2)-3=0\\ \\ \Rightarrow 6\tan(x/2)=3\\ \\ \Rightarrow \tan(x/2)=\frac{3}{6}\\ \\ \Rightarrow \tan(x/2)=\frac{1}{2}\\ \\ \Rightarrow \frac{x}{2}=\tan^{-1}\left (\frac{1}{2}  \right )$

$\Rightarrow \frac{x}{2}\approx 0.4636\\ \\ \text{the period of tangent is }\pi, \text{ so we have}\\ \\ \Rightarrow \frac{x}{2}\approx 0.4636+n\pi\\ \\ \Rightarrow x=2( 0.4636+n\pi)\\  \\ \Rightarrow x=0.9273+2n\pi\\ \\ \text{Hence the x-itnercepts of the function are: }(0.9273+2n\pi,\ 0)$