Concept explainers
To calculate: The cosecant trigonometric function
Answer to Problem 44E
The cosecant trigonometric function
Explanation of Solution
Given information:
The trigonometric functions
Formula used:
Coordinate plane is divided into four quadrants.
In the first quadrant all trigonometric functions that is
In the second quadrant only sine and cosecant trigonometric functions that is
In the third quadrant only tangent and cotangent trigonometric functions that is
In the fourth quadrant only cosine and secant trigonometric functions that is
The Pythagorean identity
Calculation:
Consider the provided trigonometric functions
To write the secant function in terms of tangent trigonometric function.
Recall the Pythagorean identity
Take square root on both the sides and simplify,
Since
Recall that coordinate plane is divided into four quadrants.
In the third quadrant only tangent and cotangent trigonometric functions that is
That is cosecant trigonometric function is negative.
Therefore,
Thus, the cosecant trigonometric function
Chapter 6 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning