Secant, Cosecant and Cotangent

In these lessons we will look at the reciprocal trigonometric functions: secant, cosecant and cotangent.

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Trigonometric Functions
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Lessons On Trigonometry
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We can get three more trigonometric functions by taking the reciprocals of three basic functions: sine, cosine and tangent.

The secant function is the reciprocal of the cosine function. The abbreviation of secant is sec.

The cosecant function is the reciprocal of the sine function. The abbreviation of cosecant is csc or cosec.

The cotangent function is the reciprocal of the tangent function. The abbreviation of cotangent is cot.

The following diagram shows the Reciprocal Trigonometric Functions. Scroll down the page for more examples and solutions on how to use the reciprocal trigonometric functions.

reciprocal trig functions

Given that , and that θ is acute, find, without using a calculator, the value of
a) sec θ
b) cot θ

We can use the Pythagorean theorem to get the third side of the right triangle.

a) We then get that

b) We have



Reciprocal Ratios: Cosecant, Secant, Cotangent.

Opposite Sides, Adjacent Sides and Hypotenuse of a Right Triangle
Definition of Cos, Sin, Tan, Csc, Sec, Cot

Find the Cosecant of an Angle in a Right Triangle
Given any two sides of a right triangle, you can find any of the 6 trigonometric ratios. This problem demonstrates how to determine the cosecant of a right triangle. Using the Pythagorean Theorem to find a missing side is demonstrated.

Reciprocal Identities of Trig Functions
This tutorial covers the reciprocal identities and shows them in various forms.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
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