Trigonometric Reciprocal Identities Math

Sin 30 csc 30 2 are reciprocals therefore sin and cosecant are reciprocals.

Trigonometric reciprocal identities math. Sine and cosecant functions. These can be trivially true like x x or usefully true such as the pythagorean theorem s a 2 b 2 c 2 for right triangles. Another way to describe reciprocals is to point out that the product of a number and its reciprocal is 1. Sin function is a reciprocal function of cosecant and cosecant function is also a reciprocal of sine function.

1 sin theta dfrac 1 csc theta. The six right triangle reciprocal identities are defined below. We have the basic trigonometric functions. Secant cosecant and cotangent are technically the three reciprocal functions but you can write identities to show their reciprocals too.

0 circ theta frac pi 2 0 θ 2π. The simplest and most basic trig identities equations of equivalence are those involving the reciprocals of the trigonometry functions. Sin θ b c cos θ a c tan θ b a. Trigonometric identities trig identities are equalities that involve trigonometric functions that are true for all values of the occurring variables.

To jog your memory a reciprocal of a number is 1 divided by that number for example the reciprocal of 2 is 1 2. Every trigonometric function has a reciprocal relation with another trigonometric function. Summary of trigonometric identities reciprocal identities sin 1 csc cos 1 sec tan 1 cot csc 1 sin sec 1 cos cot 1 tan quotient identities tan sin cos cot cos sin pythagorean identities 1 sin2 cos2 sec2 tan2 1 csc2 1 cot2. Begin array c sin theta frac b c cos theta frac a c tan theta frac b a end array.

Let s use sine and its reciprocal cosectant as an example of how the identities work. These identities are useful when we need to simplify expressions involving trigonometric functions. There are loads of trigonometric identities but the following are the ones you re most likely to see and use.