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Secant, Cosecant and Cotangent

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

Related Topics:
More Topics on Trigonometry

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.

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


Theta is in the first quadrant.
We can use Pythagoras theorem to get the third side.

a) We then get that

b) We have



Reciprical 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.


You can use the Mathway widget below to practice Trigonometry or other math topics. Try the given examples, or type in your own problem. Then click "Answer" to check your answer.

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