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The product of any object and its reciprocal is always the identity. In the case of numbers, 1 (one).

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Q: What is the product of a trigonometric function and its reciprocal?
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Related questions

What is a reciprocal trig function?

A reciprocal trigonometric function is the ratio of the reciprocal of a trigonometric function to either the sine, cosine, or tangent function. The reciprocal of the sine function is the cosecant function, the reciprocal of the cosine function is the secant function, and the reciprocal of the tangent function is the cotangent function. These functions are useful in solving trigonometric equations and graphing trigonometric functions.


What is a cotangent?

Cotangent is a trigonometric function. It is the reciprocal of the tangent.


A function whose graph is not a straight line?

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The sine of an angle is the cosine of its complement and conversely. The tan of an angle is the reciprocal of its complement.


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In Mathematics, "reciprocal" defines a quantity or function related to another so that their product is one. 2/3 is the reciprocal of 3/2 and vice versa.


Is the reciprocal of a product the product of a reciprocal?

Yes.


Why is the secant function is an even function and the tangent and cosecant are odd functions?

I find it convenient to express other trigonometric functions in terms of sine and cosine - that tends to simplify things. The secant function is even because it is the reciprocal of the cosine function, which is even. The tangent function is the sine divided by the cosine - an odd function divided by an even function. Therefore it is odd. The cosecant is the reciprocal of an odd function, so it is naturally also an odd function.


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