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Problem 705

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.

Expert verified

A polar equation \(r = f(θ)\) is symmetric about (a) the polar axis if \(r = f(-θ)\), (b) the \(90^{\circ}\)-axis if \(r = f(\frac{π}{2} - θ)\), and (c) the pole if \(-r = f(θ + π)\) or \(r = f(θ + π)\).

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Chapter 41

Given the equation \(\mathrm{x}^{2}-\mathrm{y}^{2}=1\), translate to polar coordinates and draw a sketch of the curve using the polar equation.

Chapter 41

Convert the measures $30^{\circ}, 45^{\circ}, 60^{\circ}, 90^{\circ}, 180^{\circ}$ from degrees to radians.

Chapter 41

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

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.

Chapter 41

Graph \(\mathrm{r}=\sin 3 \theta\)

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