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Va? – x²

Va? – x²

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Express in terms of a trigonometric function of θ, without radicals by making the trigonometric substitution x=a cos θ for π < θ <2π and a >0.

The image displays a mathematical expression under a square root symbol: \(\sqrt{a^2 - x^2}\). ### Explanation: This expression represents the square root of the difference between \(a^2\) and \(x^2\). It often appears in problems dealing with circles, ellipses, and trigonometry. Understanding this expression is essential in applications such as calculating the length of a segment in a circle or simplifying integrals in calculus. #### Applications: - **Geometry**: In the context of a circle with radius \(a\), this represents the distance from a point on the x-axis to a point on the circle. - **Trigonometry**: This expression often appears in the context of computing the sine or cosine of an angle when dealing with right triangles. - **Calculus**: It is used in integral expressions for finding arc lengths or solving certain types of differential equations. Understanding how to manipulate and work with this expression is essential for advanced mathematical problem-solving.
Transcribed Image Text:The image displays a mathematical expression under a square root symbol: \(\sqrt{a^2 - x^2}\). ### Explanation: This expression represents the square root of the difference between \(a^2\) and \(x^2\). It often appears in problems dealing with circles, ellipses, and trigonometry. Understanding this expression is essential in applications such as calculating the length of a segment in a circle or simplifying integrals in calculus. #### Applications: - **Geometry**: In the context of a circle with radius \(a\), this represents the distance from a point on the x-axis to a point on the circle. - **Trigonometry**: This expression often appears in the context of computing the sine or cosine of an angle when dealing with right triangles. - **Calculus**: It is used in integral expressions for finding arc lengths or solving certain types of differential equations. Understanding how to manipulate and work with this expression is essential for advanced mathematical problem-solving.
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