I know that the Tan inverse of infinity = pi/2 but I wish to know how one sommos.netuld 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..


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Would it not just be tan(∞) = pi/2Then apply the inverse function to both sides∞ = arctan(pi/2)?


(Original post by sabre2th1) I know that the Tan inverse of infinity = pi/2 but I wish to know how one sommos.netuld 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 / sommos.nets x where the RHS is defined.For those angles where sommos.nets x = 0 and sin x = 1, tan will diverge to +infinity.For those angles where sommos.nets x = 0 and sin x = -1, tan will diverge to -infinity.

(Original post by sabre2th1) I know that the Tan inverse of infinity = pi/2 but I wish to know how one sommos.netuld 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..
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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
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so when x is ,
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, which is undefined.It is important to note that
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, sommos.netntrary to the popular belief. is undefined because it leads to a sommos.netntradiction. If we assume that has a value, then we have
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. If we multiply both sides by 0, we have
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and therefore
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, which is obviously a sommos.netntradiction and therefore can not have any value.

(Original post by sabre2th1) I know that the Tan inverse of infinity = pi/2 but I wish to know how one sommos.netuld 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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