SOLUTION: Is there a real number for x such that- cosec(x) = sin(1/x)

Question 847501: Is there a real number for x such that-
cosec(x) = sin(1/x)
Answer by swincher4391(1107) (Show Source): You can put this solution on YOUR website!
csc(x) = sin(1/x)
1/sin(x) = sin(1/x)
This implies that 1 = sin(x) * sin(1/x)
Since sin(x) ranges from -1 to 1 and sin(1/x) ranges from -1 to 1, the only possible multiplication is if sin(x)= 1 and sin(1/x)= 1
Well if sin(x) = 1, then we find x = pi/2 or 90 degrees.
However when we plug this same x value back into sin(1/x):
sin(2/pi) does not = 1. It equals .594.
Since our only possible situation did not pan out, it is safe to assume that there is NO SOLUTION that satisfies this.

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