Concept explainers
Find the Trigonometric functions are even and odd.
Answer to Problem 5E
Sine, cosecant, tangent and cotangent are odd functions.
Cosine and Secant are even functions.
Explanation of Solution
Given:
Concept Used:
Even Functions
A function is "even" when: f(x) = f(-x) for all x.
In other words there is symmetry about the y-axis (like a reflection):
In Trigonometry Cosine and Secant functions are Even Function.
Odd Functions
A function is "odd" when: f(-x) = -f(x) for all x
Note the minus in front of f(x): -f(x), And we get origin symmetry:
In Trigonometry, the sine, cosecant, tangent and cotangent functions are odd functions .
Calculation:
Sine is an odd function, and cosine is an even function. A function f is said to be an odd function if for any number x, f(−x) = −f(x).
Sine , Cosecant , Tangent and Cotangent are odd functions.
Cosine and Secant are even functions.
Thus, Sine, cosecant, tangent and cotangent are odd functions and Cosine and Secant are even functions.
Chapter 4 Solutions
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
- 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