Concept explainers
(A)
To prove:
The function is periodic
(A)
Explanation of Solution
Given:
The function is periodic
Concept used:
The functions tangent and cotangent have period
The functions cosecant and secant have period
Calculation:
Since the tangent and cotangent function have period
The function
Complete one period as
That is for
Solving this inequality
So each period is
The functions tangent have period
If the point satisfies the function then shade the entire region to denote that every point in the region satisfies the function
(B)
To prove:
The function is periodic
(B)
Explanation of Solution
Given:
The function is periodic
Concept used:
The functions tangent and cotangent have period
The functions cosecant and secant have period
Calculation:
Since the tangent and cotangent function have period
The function
Complete one period as
That is for
Solving this inequality
So each period is
The functions tangent have period
The functions tangent and cotangent have period
The functions cosecant and secant have period
Chapter 5 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