Concept explainers
To calculate: The cosine trigonometric function
Answer to Problem 41E
The cosine 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 cosine function in terms of sine trigonometric function.
Recall the Pythagorean identity
Subtract
Since
Recall that coordinate plane is divided into four quadrants.
In the fourth quadrant only cosine and secant trigonometric functions that is
That is cosine trigonometric function is positive.
Therefore,
Thus, the cosine 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