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# why tan(90)=inf

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why tan(90) equals infinity?

Dec 30, 2018

#1
+103131
+3

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°

Dec 30, 2018
#2
+103695
+2

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.

AND

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
#3
+103695
+2

I should not have used the = sign.

tan90 does not equal undefined it just IS undefined

Melody  Dec 30, 2018