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Magazine Problem 53
Sketch a graph of the rectangular equation. [Hint: First convert the equation to polar coordinates.] $$ \left(x^{2}+y^{2}\right)^{3}=4 x^{2} y^{2} $$
Problem 54
Convert the polar equation to rectangular coordinates. $$ r=2 \csc \theta $$
Problem 54
Find the product \(z_{1} z_{2}\) and the quotient \(z_{1} / z_{2}\) . Express your answer in polar form. $$ z_{1}=\cos \frac{\pi}{4}+i \sin \frac{\pi}{4}, \quad z_{2}=\cos \frac{3 \pi}{4}+i \sin \frac{3 \pi}{4} $$
Problem 54
Sketch a graph of the rectangular equation. [Hint: First convert the equation to polar coordinates.] $$ \left(x^{2}+y^{2}\right)^{3}=\left(x^{2}-y^{2}\right)^{2} $$
Problem 55
Convert the polar equation to rectangular coordinates. $$ r=4 \sin \theta $$
Problem 55
Find the product \(z_{1} z_{2}\) and the quotient \(z_{1} / z_{2}\) . Express your answer in polar form. $$ z_{1}=3\left(\cos \frac{\pi}{6}+i \sin \frac{\pi}{6}\right), \quad z_{2}=5\left(\cos \frac{4 \pi}{3}+i \sin \frac{4 \pi}{3}\right) $$
Problem 55
Sketch a graph of the rectangular equation. [Hint: First convert the equation to polar coordinates.] $$ \left(x^{2}+y^{2}\right)^{2}=x^{2}-y^{2} $$
Problem 56
Convert the polar equation to rectangular coordinates. $$ r=6 \cos \theta $$
Problem 56
Find the product \(z_{1} z_{2}\) and the quotient \(z_{1} / z_{2}\) . Express your answer in polar form. $$ z_{1}=7\left(\cos \frac{9 \pi}{8}+i \sin \frac{9 \pi}{8}\right), \quad z_{2}=2\left(\cos \frac{\pi}{8}+i \sin \frac{\pi}{8}\right) $$
Problem 56
Sketch a graph of the rectangular equation. [Hint: First convert the equation to polar coordinates.] $$ x^{2}+y^{2}=\left(x^{2}+y^{2}-x\right)^{2} $$
