Concept explainers
To explain: how the length of the intercepted arc change when the radius of a circle increases and the magnitude of a central angle is held constant.
Answer to Problem 75E
Arc length is proportional to the radius of circle.
Explanation of Solution
Concept Used:
For a circle of radius r , the arc length s of the sector with central angle
For the variables x and y , the statement y varies directly as x can be translated as:
Where k is a non-zero constant called the constant of proportionality.
Now, the arc length of the circle is,
And here the magnitude of a central angle is held constant.
Then it satisfies above definition of being proportional.
Hence, it can be said that if the magnitude of a central angle is held constant, then the arc length is proportional to the radius of circle.
Chapter 4 Solutions
EBK PRECALCULUS W/LIMITS
- 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