91Ó°ÊÓ

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

Graph the complex number and find its modulus. $$5+2 i$$

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

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 \(r>0\). $$(2,3 \pi / 4)$$

Test the polar equation for symmetry with respect to the polar axis, the pole, and the line \(\theta=\pi / 2\) $$r=4+8 \cos \theta$$

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. $$x=t+1, \quad y=\frac{t}{t+1}$$

Graph the complex number and find its modulus. $$7-3 i$$

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 \(r>0\). $$(-1,7 \pi / 6)$$

Test the polar equation for symmetry with respect to the polar axis, the pole, and the line \(\theta=\pi / 2\) $$r=3 \sec \theta$$

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. $$x=4 t^{2}, \quad y=8 t^{3}$$