Explanation Given Information: The polar equation r = 1 − sin θ . Formula used: Test for symmetry: Polar axis: replace θ with − θ in the provided equation. The line θ = π 2 : replace ( r , θ ) with ( − r , − θ ) in the provided equation. The pole: replace r with − r in the provided equation Calculation: To check for the symmetry of r = 1 − sin θ , apply each of the tests of symmetry. To check for the symmetry along polar axis, replace θ by − θ in r = 1 − sin θ : r = 1 − sin ( − θ ) As, sine function is odd function. So, r = 1 − sin ( − θ ) r = 1 − ( − sin θ ) r = 1 + sin θ Because the polar equation changes on replacing θ by − θ , the equation fails this symmetry test. Thus, r = 1 − sin θ may or may not be symmetric about polar axis. To check for the symmetry along the line θ = π 2 , replace ( r , θ ) by ( − r , − θ ) in r = 1 − sin θ − r = 1 − sin ( − θ ) As, sine function is odd function. So, − r = 1 − sin ( − θ ) − r = 1 + sin θ r = − ( 1 + sin θ ) Because the polar equation changes on replacing ( r , θ ) by ( − r , − θ ) , the equation fails this symmetry test. Thus, r = 1 − sin θ may or may not be symmetric along the line θ = π 2 . To check for the symmetry about the pole, replace r by − r in r = 1 − sin θ − r = 1 − sin θ r = sin θ − 1 Because the polar equation changes on replacing r by − r , the equation fails this symmetry test. Thus, r = 1 − sin θ may or may not be symmetric with respect to pole. Graph: Consider the given polar equation r = 1 − sin θ . As, the period of the sine function is 2 π , it is not required to consider values of θ beyond 2 π . Calculate the value of r for some values of θ from 0 t o 2 π

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ISBN: 8220103679510

Author: Blitzer

Publisher: PEARSON

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Chapter 11.2, Problem 88PE

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To calculate: The symmetry of r=1−sinθ and sketch its graph.

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Chapter 11.2, Problem 87PE

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Chapter 11 Solutions

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Ch. 11.1 - Check Point 1 Find: . Ch. 11.1 - Prob. 2CP Ch. 11.1 - Prob. 3CP Ch. 11.1 - Prob. 4CP Ch. 11.1 - Prob. 5CP Ch. 11.1 - Prob. 1CVC Ch. 11.1 - Prob. 2CVC Ch. 11.1 - Prob. 3CVC Ch. 11.1 - Fill in each blank so that the resulting statement...Ch. 11.1 - Fill in each blank so that the resulting statement...

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The symmetry of r = 1 − sin θ and sketch its graph.

Solution Summary: The author explains how the polar equation r=1-mathrmsintheta failed the test for symmetry about the pole and its graph.

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