Concept explainers
To calculate: The value oftheexpression
Answer to Problem 40E
The value of trigonometric expression
Explanation of Solution
Given information:
The expression
Formula used:
Inverse tangent trigonometric function is expressed as
Domain of inversetangent trigonometric function is
Calculation:
Consider the expression
Observe from the above expression that x approaches 0 from right hand side on coordinate axes. So, the logarithmic function tends to negative infinity as x approaches 0 from right hand side.
Now, in a right angled triangle an angle must be there which gives a very large negative value for opposite of side triangle divided by the adjacent side of the triangle.
This is only possible when one of the angles in a right angled triangle approaches
Recall that the inverse tangent trigonometric function is expressed as
Recall that value of tangent function at an angle
That is,
Therefore,
Thus, the value of trigonometric expression
Chapter 3 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced 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