How can we say that $\tan90^\circ=+\infty?$ Usually we take, $$\tan90^\circ=+\infty$$ 
But how fair is it? From the tan curve we get $\tan90^\circ$ is inditerminate. Can someone explain please?
 A: The tangent of $90^{\circ}$ is undefined. $\tan 90^{\circ}=\infty$ is a shorthand way of saying that as $\theta$ gets very close to $90^{\circ},\ \tan \theta$ becomes arbitrarily large; it isn't meant to be taken literally.  You'll see a more detailed discussion of this phenomenon when you take calculus.  
A: The query "tangent special values" on Google images shows numerous tables of values. Most of them say "not defined", "undefined" or "-" for $\tan 90°$. I saw one with $\pm\infty$, one with "Infinity", and another with $\infty$.
I bet that $+\infty$ is even more scarce and IMO would be a true mistake. So this "usually" is excessive.
By default, Wolfram Alpha considers complex numbers and reports $\tilde\infty$, the complex infinity.
Interestingly, Microsoft Mathematics returns "Indeterminate" in the real mode, and $\tilde\infty$ in the complex one, while the Calculator just says "Invalid input".
A: If you've ever seen this, it was abbreviating a left-hand limit; the right-hand limit is if course $-\infty$. Depending on the context, one might only care about a one-sided limit.
A: IMO, $\tan 90°=+\infty$ is wrong because the positive sign is enforced, whereas this only makes sense for the left-side limit.
$\tan 90°=\pm\infty$ and, more loosely $\tan 90°=\infty$ are more acceptable as they leave room for the indeterminate sign.
In any case, we admit that $\tan90°$ is short for $\lim_{\theta\to90°}\tan\theta$.
