Secant, Cosecant and Cotangent
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More Topics on Trigonometry
In these lessons we will look at the reciprocal trigonometric functions: secant, cosecant and cotangent.
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 Reciprocal Trigonometric Functions are as follows:
Example:
Given that
, and that θ is acute, find, without using a calculator, the value of
a) sec θ
b) cot θ
a) We then get that
b) We have
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 free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
More Topics on Trigonometry
In these lessons we will look at the reciprocal trigonometric functions: secant, cosecant and cotangent.
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 Reciprocal Trigonometric Functions are as follows:
Example:Given that
, and that θ is acute, find, without using a calculator, the value ofa) sec θ
b) cot θ
Solution:
We can use the Pythagorean theorem to get the third side of the right triangle.a) We then get that
b) We have
Videos
Reciprocal Ratios: Cosecant Secant Cotangent. Opposite Sides, Adjacent Sides and Hypotenuse of a Right TriangleDefinition 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.
Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.
You can use the free Mathway calculator and problem solver below to practice Algebra or other 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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