Finding the range of a function Find the range of $y=\tan \theta$ for $0<\theta<90$.
I drew the function out, and see that the function will be between $\tan 0 < y < \tan90$ but $\tan 90$ is undefined so what would the range be?
Thanks

The range of $y = \tan \theta$ for $0 \lt \theta \lt 90^\circ$ is the set of all positive real numbers:
i.e., the range is all of the open interval $(0, + \infty)$.
Below is the graph of $y = \tan \theta$ where $\theta$ ranges from $0$ to $\pi/2 = 90^\circ$ (source: Wolfram Alpha). Graphs always help to develop intuition regarding the range of functions, particularly trigonometric functions. We see that as $\theta$ increases and approaches $\pi/2$ radians $= 90^\circ$, $y = \tan\theta$ will grow without bound.


You can also ask WolframAlpha for the range directly and even restrict to a specified domain as in range of tan(x) restricted to 0<=x<90 degrees:

