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sin(pi/2)=infinity/infinity

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So i have a problem here. I will probably answer myself to this question after some time, but anyways i will post it here.  So folow the logic i have here. In picture you can see right-angled triangle. Let angle between c1 and h be α. Then c2/h = sin(α) . If α increases then so do length of c2 and length of h. If α=90 degrees then c2 is with infinity length, and so is h=infinity.  so we get that sin(pi/2) = infinity/infinity, which should be undefined, but it is 1. Why?