Answer by user160738 for Finding the range and domain of $f(x)=\tan (x)$
This really is up to how rigourous you want to be. Your ideas on showing that $\tan(x)$ diverging to when $\cos(x)$ tends to 0 is fine, but rigourous proof would start from definition of 'tending to...
View ArticleAnswer by Taladris for Finding the range and domain of $f(x)=\tan (x)$
When $\theta$ is in $dom(\tan)={\mathbb R}\setminus (\frac{\pi}{2}+\pi{\mathbb Z})$, then $tan(\theta)$ is the slope of the line through the origin and the point $(\cos(\theta),\sin(\theta))$. Since we...
View ArticleAnswer by Mathmo123 for Finding the range and domain of $f(x)=\tan (x)$
Firstly, I'd like to applaud you on your persistence in trying to get to a rigorous solution.I'll give you a hint for a geometric solution: if you use the triangle definition of a tangent, can you...
View ArticleAnswer by Prahlad Vaidyanathan for Finding the range and domain of $f(x)=\tan...
It is easiest to use the intermediate value theorem when finding the range : You know that$$\lim_{x\to \pi/2} \tan(x) = +\infty \text{ and } \lim_{x\to -\pi/2} \tan(x) = -\infty$$So the image of the...
View ArticleFinding the range and domain of $f(x)=\tan (x)$
I am attempting to find the range and domain of $f(x)=\tan(x)$ and show why this is the case. I can seem to find the domain relatively well, however I run into problems with the range. Here's what I...
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