91Ó°ÊÓ

Test the polar equation for symmetry with respect to the polar axis, the pole, and the line \(\theta=\pi / 2 .\) $$ r=5 \cos \theta \csc \theta $$

Graph the complex number and find its modulus. $$ -1-\frac{\sqrt{3}}{3} i $$

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 \(r>0\) . $$ (-2,-\pi / 3) $$

\(3-24=A\) 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. $$ x=|t|, \quad y=|1-| t| | $$

Test the polar equation for symmetry with respect to the polar axis, the pole, and the line \(\theta=\pi / 2 .\) $$ r=\frac{4}{3-2 \sin \theta} $$

Graph the complex number and find its modulus. $$ \frac{3+4 i}{5} $$

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 \(r>0\) . $$ (-5,0) $$

\(3-24=A\) 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. $$ x=2 \sin t, \quad y=2 \cos t, \quad 0 \leq t \leq \pi $$

Graph the complex number and find its modulus. $$ \frac{-\sqrt{2}+i \sqrt{2}}{2} $$

Test the polar equation for symmetry with respect to the polar axis, the pole, and the line \(\theta=\pi / 2 .\) $$ r=\frac{5}{1+3 \cos \theta} $$