91Ó°ÊÓ

\(3-24=A\) pair of parametric equations is given. (a) Sketch the curve represented by the parametric equations. (b) Find a rectangular coordinate equation for the curve by eliminating the parameter. $$ x=2 \cos t, \quad y=3 \sin t, \quad 0 \leq t \leq 2 \pi $$

Plot the point that has the given polar coordinates. Then give two other polar coordinate representations of the point, one with \(r<0\) and the other with \(r>0\) . $$ (3,1) $$

Test the polar equation for symmetry with respect to the polar axis, the pole, and the line \(\theta=\pi / 2 .\) $$ r^{2}=4 \cos 2 \theta $$

\(3-24=A\) pair of parametric equations is given. (a) Sketch the curve represented by the parametric equations. (b) Find a rectangular coordinate equation for the curve by eliminating the parameter. $$ x=\sin ^{2} t, \quad y=\sin ^{4} t $$

Sketch the complex number \(z,\) and also sketch \(2 z,-z\) and \(\frac{1}{2} z\) on the same complex plane. $$ z=1+i $$

\(3-24=A\) pair of parametric equations is given. (a) Sketch the curve represented by the parametric equations. (b) Find a rectangular coordinate equation for the curve by eliminating the parameter. $$ X=\sin ^{2} t, \quad y=\cos t $$

Different Polar Coordinates for the Same Point: Plot the point that has the given polar coordinates. Then give two other polar coordinate representations of the point, one with \(r<0\) and the other with \(r>0\). (3,1)

Test the polar equation for symmetry with respect to the polar axis, the pole, and the line \(\theta=\pi / 2 .\) $$ r^{2}=9 \sin \theta $$

Sketch the complex number \(z,\) and also sketch \(2 z,-z\) and \(\frac{1}{2} z\) on the same complex plane. $$ z=-1+i \sqrt{3} $$

Sketch the complex number \(z\) and its complex conjugate \(z\) on the same complex plane. $$ z=8+2 i $$