91Ó°ÊÓ

Convert the polar equation to rectangular coordinates. $$r=1+\cos \theta$$

Show that the graph of \(r=a \cos \theta+b \sin \theta\) is a circle, and find its center and radius.

Find the product \(z_{1} z_{2}\) and the quotient \(z_{1} / z_{2}\). Express your answer in polar form. $$z_{1}=4\left(\cos 120^{\circ}+i \sin 120^{\circ}\right)$$ $$z_{2}=2\left(\cos 30^{\circ}+i \sin 30^{\circ}\right)$$

Find the product \(z_{1} z_{2}\) and the quotient \(z_{1} / z_{2}\). Express your answer in polar form. $$z_{1}=\sqrt{2}\left(\cos 75^{\circ}+i \sin 75^{\circ}\right)$$ $$z_{2}=3 \sqrt{2}\left(\cos 60^{\circ}+i \sin 60^{\circ}\right)$$

Convert the polar equation to rectangular coordinates. $$r=3(1-\sin \theta)$$

(a) Graph the polar equation \(r=\tan \theta \sec \theta\) in the viewing rectangle \([-3,3]\) by \([-1,9]\) (b) Note that your graph in part (a) looks like a parabola (see Section 2.5 ). Confirm this by converting the equation to rectangular coordinates.

Find the product \(z_{1} z_{2}\) and the quotient \(z_{1} / z_{2}\). Express your answer in polar form. $$z_{1}=4\left(\cos 200^{\circ}+i \sin 200^{\circ}\right)$$ $$z_{2}=25\left(\cos 150^{\circ}+i \sin 150^{\circ}\right)$$

Convert the polar equation to rectangular coordinates. $$r=1+2 \sin \theta$$

Convert the polar equation to rectangular coordinates. $$r=2-\cos \theta$$

Find the product \(z_{1} z_{2}\) and the quotient \(z_{1} / z_{2}\). Express your answer in polar form. $$z_{1}=\frac{4}{5}\left(\cos 25^{\circ}+i \sin 25^{\circ}\right)$$ $$z_{2}=\frac{1}{3}\left(\cos 155^{\circ}+i \sin 155^{\circ}\right)$$