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# Tan inverse of infinity watch

1. I know that the Tan inverse of infinity = pi/2 but I wish to know how one could arrive at the RHS manually (i.e. without using tools such as wolfram alpha)..

I sketched a graph of tan^-1(x) but I have not managed to progress. I'm probably missing something quite basic..
2. Would it not just be tan(∞) = pi/2

Then apply the inverse function to both sides

∞ = arctan(pi/2)

?
3. Infinity is not a number. You can't do that. The graph never reaches infinity.
4. (Original post by sabre2th1)
I know that the Tan inverse of infinity = pi/2 but I wish to know how one could arrive at the RHS manually (i.e. without using tools such as wolfram alpha)..

I sketched a graph of tan^-1(x) but I have not managed to progress. I'm probably missing something quite basic..
tan x = sin x / cos x where the RHS is defined.

For those angles where cos x = 0 and sin x = 1, tan will diverge to +infinity.
For those angles where cos x = 0 and sin x = -1, tan will diverge to -infinity.
5. (Original post by sabre2th1)
I know that the Tan inverse of infinity = pi/2 but I wish to know how one could arrive at the RHS manually (i.e. without using tools such as wolfram alpha)..

I sketched a graph of tan^-1(x) but I have not managed to progress. I'm probably missing something quite basic..

The value of tan(x) approaches positive infinity as x approaches (and negative infinity if you approach it the other way around), but it never reaches infinity. Remember that so when x is , , which is undefined.

It is important to note that , contrary to the popular belief. is undefined because it leads to a contradiction. If we assume that has a value, then we have . If we multiply both sides by 0, we have and therefore , which is obviously a contradiction and therefore can not have any value.
6. (Original post by sabre2th1)
I know that the Tan inverse of infinity = pi/2 but I wish to know how one could arrive at the RHS manually (i.e. without using tools such as wolfram alpha)..

I sketched a graph of tan^-1(x) but I have not managed to progress. I'm probably missing something quite basic..
Tan is undefined at pi/2, as you reach different limits approaching it from the left and from the right.

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