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Problem 710

Graph the curve \(\mathrm{r}=2+2 \cos \theta\).

Expert verified

To graph the curve \(r = 2 + 2\cos\theta\), plot critical points such as (4, 0), (2, π/2), (0, π), (2, 3π/2), and (4, 2π) in the polar coordinate system. Connect these points smoothly to form a loop shape known as a limaçon, which has symmetry with respect to the polar axis. The graph should show the curve originating from the point (4,0), extending above and below the polar axis, and closing back at the same point (4,0).

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Chapter 41

Given the line \(\mathrm{y}=\mathrm{mx}+\mathrm{b}\) in Cartesian coordinates, find its polar equation.

Chapter 41

Find the conditions which the equation of a polar figure must satisfy for the figure to be (a) symmetric about the polar axis, (b) symmetric about the \(90^{\circ}\) -axis, (c) symmetric about the pole.

Chapter 41

Graph the curve \(\mathrm{r}=2 \cos \theta\)

Chapter 41

By a rotation of the coordinate axes, transform the equation $$ 9 x^{2}-24 x y+16 y^{2}-40 x-30 y=0 $$ into another equation lacking the cross product term. (Plot the locus and draw both sets of axes.)

Chapter 41

Transform the equation $2 \mathrm{x}^{2}+\sqrt{3} \mathrm{xy}+\mathrm{y}^{2}=4$ by rotating the coordinate axes through an angle of \(30^{\circ}\). Plot the locus and show both sets of axes.

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