TEF - The Reciprocal and Quotient Identities Lesson

The Reciprocal and Quotient Identities

Along with sine, cosine and tangent, there are three additional trigonometric identities we will use in Precalculus. They are the reciprocal identities:

Cosecant: $\csc\theta=\frac{r}{y},\:y\ne0$ Secant: $\sec\theta=\frac{r}{x},\:x\ne0$ Cotangent: $\cot\theta=\frac{x}{y},\:y\ne0$

Use your unit circle to find the following: Hover over each statement for the solution.

An identity is an equation that is true for all values of the variable for which the expressions in the equation are defined. When we have identities, we can use them to simplify or change expressions by interchanging equivalent values. The reciprocal identities are called such because they are the reciprocals of the 3 main trig functions you already know:

In addition to the reciprocal identities, we can derive the quotient identities. See reasoning for the tangent identity below:

Watch this video, to see how you can use reciprocal identities to verify identity statements.

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