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The reciprocal of sine is sin(-1).

-1 being above the sin in small text like a squared number.

* * * * *

NO!

sin-1 is the inverse function of sin, and that is not the same as the reciprocal. The reciprocal of sin(x) is 1/(sin(x) which is cosec(x).

The following simple example will illustrate the difference between a reciprocal and inverse.

Consider the function which doubles the value of its argument.

That is f(x) = 2x

The inverse of f(x) is the function g which halves its argument ie g(x) = x/2.

The function g(x) reverses the action of f(x) and f(x) reverses g(x).

Thus f[g(x)] = x for all x.

The reciprocal of f(x) is 1/f(x) = 1/2x.

So that for any value x, f(x) multiplied by its reciprocal (if it exists) always equals 1.

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Q: What is sine reciprocal?
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