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The cosecant is the reciprocal of the sine function. Now, the reciprocal of a positive number is positive, and the reciprocal of a negative number is negative.
It does not work that way. A negative power is simply the reciprocal. So that x-a = 1/xa The reciprocal is negative or positive according to whether the number itself is negative or positive. [And, if the number is 0, the reciprocal is not defined.]
Yes.
1 is the only positive number that is its own reciprocal. -1 is the negative number that is its own reciprocal.
You multiply the negative number by the reciprocal of the fraction.