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Magazine Problem 29
Sketch the curve with the given polar equation by first sketching the graph of \(r\) as a function of \(\theta\) in Cartesian coordinates. $$r=4 \sin 3 \theta$$
Problem 29
Find all points of intersection of the given curves. $$r=1+\sin \theta, \quad r=3 \sin \theta$$
Problem 29
Find the area enclosed by the \(x\) -axis and the curve \(x=1+e^{t}, y=t-t^{2}\)
Problem 30
Find the area of the region enclosed by the astroid \(x=a \cos ^{3} \theta, y=a \sin ^{3} \theta\)
Problem 30
Find all points of intersection of the given curves. $$r=\cos 3 \theta, \quad r=\sin 3 \theta$$
Problem 30
Sketch the curve with the given polar equation by first sketching the graph of \(r\) as a function of \(\theta\) in Cartesian coordinates. $$r=\cos 5 \theta$$
Problem 31
Find all points of intersection of the given curves. $$r=\sin \theta, \quad r=\sin 2 \theta$$
Problem 31
Sketch the curve with the given polar equation by first sketching the graph of \(r\) as a function of \(\theta\) in Cartesian coordinates. $$r=2 \cos 4 \theta$$
Problem 31
\(31-32=\) Compare the curves represented by the parametric equations. How do they differ? $$\text (a) x=t^{3}, \quad y=t^{2} \quad (b) x=t^{6}, \quad y=t^{4}\text (c) x=e^{-3 t}, \quad y=e^{-2 t}$$
Problem 32
\(31-32=\) Compare the curves represented by the parametric equations. How do they differ? $$ \begin{array}{ll}{\text { (a) } x=t,} & {y=t^{-2} \quad \text { (b) } x=\cos t, \quad y=\sec ^{2} t} \\ {\text { (c) } x=e^{t},} & {y=e^{-2 t}}\end{array} $$
