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why tan(90) equals infinity?

 Dec 30, 2018

It doesn't = "infinity"   [ this is what many calculators show ]


It would be better said that it is "undefined"


The tangent ratio is  y / x


But, at 90°, y will = r, but x = 0......and since we cannot dvide by 0, then thr tangent is undefined at 90°



cool cool cool

 Dec 30, 2018

Here is the graph of y=tanx


You can see that as x tends to 90 degrees from below   the tan of it approaches +infinity.


as x tends to 90 from above x tends to - infinity.



So it is correct to say this


\(\displaystyle\lim_{x\rightarrow \infty^-}\;\;tanx=+\infty\\~\\ \displaystyle\lim_{x\rightarrow \infty^+}\;\;tanx=-\infty\\~\\ but\\ \displaystyle\lim_{x\rightarrow \infty}\;\;tanx=\text{undefined}\)

 Dec 30, 2018
edited by Melody  Dec 30, 2018

I should not have used the = sign.

tan90 does not equal undefined it just IS undefined   wink

Melody  Dec 30, 2018

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