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4. Consider the polar function r(0) = 2+2 cos(20), for 0 E [0, 27). (a) Write parametric equations for the polar curve r = r(0), using 0 e [0, 27) as a parameter.

4. Consider the polar function r(0) = 2+2 cos(20), for 0 E [0, 27). (a) Write parametric equations for the polar curve r = r(0), using 0 e [0, 27) as a parameter.

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Consider the polar function r(0) =2+2 cos(20), for 0 E [0, 27). (a) Write parametric equations for the polar curve r = r(0), using 0 € [0, 27) as a parameter. 4.
Transcribed Image Text:Consider the polar function r(0) =2+2 cos(20), for 0 E [0, 27). (a) Write parametric equations for the polar curve r = r(0), using 0 € [0, 27) as a parameter. 4.
dy (x), the (implicit) derivative of y with respect to x, as a function dx (b) Find a general expression for of 0. (c) Find the tangent line to the curve at the point corresponding to 0 = (d) For which values of 0 does the curve have a horizontal tangent line and for which values of 0 does the curve have a vertical tangent line? Recall that you need to give exact values (i.e., you need to do the exercises without using a calculator). In this exercise, this means that some of might need to be given in terms of an inverse trigonometric function, such as arccos(x), arcsin(x) etc. (Note: recall that, if, for a certain value 0, both x'(00) and y'(0) are zero, you need to study your answers the limit y'(0) lim 0→80 x'(0) to understand the nature of the tangent line.)
Transcribed Image Text:dy (x), the (implicit) derivative of y with respect to x, as a function dx (b) Find a general expression for of 0. (c) Find the tangent line to the curve at the point corresponding to 0 = (d) For which values of 0 does the curve have a horizontal tangent line and for which values of 0 does the curve have a vertical tangent line? Recall that you need to give exact values (i.e., you need to do the exercises without using a calculator). In this exercise, this means that some of might need to be given in terms of an inverse trigonometric function, such as arccos(x), arcsin(x) etc. (Note: recall that, if, for a certain value 0, both x'(00) and y'(0) are zero, you need to study your answers the limit y'(0) lim 0→80 x'(0) to understand the nature of the tangent line.)
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