Reciprocal Identities of Trigonometry


Reciprocal Identities of Trigonometry

The simplest and most basic trigonometric identities are those involving the reciprocals of the trigonometry functions. For simplicty a reciprocal of a number is equals 1 divided by that number — for example, the reciprocal of 4 is 1/4. Another way to describe reciprocals is to point out that the product of a number and its reciprocal is always equals to 1.






When we multiply the reciprocals together, we get 1:


SinӨ x CosecӨ = 1

CosӨ x SecӨ = 1

Tan Ө x CotӨ = 1


There is an exception, that the function can’t be equal to 0; as the number 0 doesn’t have a reciprocal as it will become Infinity.

The reciprocal identity is a very useful one when we are solving trigonometric equations. If we find a way to multiply each side of an equation by a function’s reciprocal, we may be able to reduce some part of the equation to 1 — and simplifying is always a good thing in Mathematics.