Explanation The equation for the variable x is as, x = r cos θ (1) The equation for the variable y is as, y = r sin θ (2) The polar equations r = 1 + sin ( θ − π 6 ) . Substitute 1 + sin ( θ − π 6 ) for r in equation (1) as, x = r cos θ = 1 + sin ( θ − π 6 ) cos θ (3) Substitute 1 + sin ( θ − π 6 ) for r in equation (2) as, y = r sin θ = 1 + sin ( θ − π 6 ) sin θ (4) Use online graphing calculator and sketch the curves r = 1 + sin ( θ − π 6 ) , r = 1 + sin ( θ − π 3 ) and r = 1 + sin θ as shown below Figure 1

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Chapter 10.3, Problem 65E

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The relation with which the graphs r=1+sin(θ−π6) and r=1+sin(θ−π3) are related to r=1+sinθ. Also explain in general the relation between the graphs of r=f(θ−α) and r=f(θ).

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Chapter 10.3, Problem 64E

Chapter 10.3, Problem 66E

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The relation with which the graphs r = 1 + sin ( θ − π 6 ) and r = 1 + sin ( θ − π 3 ) are related to r = 1 + sin θ . Also explain in general the relation between the graphs of r = f ( θ − α ) and r = f ( θ ) .

Solution Summary: The author explains the relation between the graphs r=1+mathrmsin(theta -alpha ) and the polar equations for

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The relation with which the graphs r=1+sin(θ−π6) and r=1+sin(θ−π3) are related to r=1+sinθ. Also explain in general the relation between the graphs of r=f(θ−α) and r=f(θ).

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