91Ó°ÊÓ

Express the following polar coordinates in Cartesian coordinates. $$\left(1,-\frac{\pi}{3}\right)$$

Find the points at which the following polar curves have horizontal or vertical tangent lines. $$r=\sin 2 \theta$$

Consider the following parametric equations. a. Eliminate the parameter to obtain an equation in \(x\) and \(y\). b. Describe the curve and indicate the positive orientation. $$x=1-3 \sin 4 \pi t, y=2+3 \cos 4 \pi t ; 0 \leq t \leq 1 / 2$$

Find the points at which the following polar curves have horizontal or vertical tangent lines. $$r=3+6 \sin \theta$$

Express the following polar coordinates in Cartesian coordinates. $$\left(2, \frac{7 \pi}{4}\right)$$

Use algebraic methods to find as many intersection points of the following curves as possible. Use graphical methods to identify the remaining intersection points. $$r=2 \cos \theta \text { and } r=1+\cos \theta$$

Consider the following parametric equations. a. Eliminate the parameter to obtain an equation in \(x\) and \(y\). b. Describe the curve and indicate the positive orientation. $$x=8+2 t, y=1 ;-\infty

Express the following polar coordinates in Cartesian coordinates. $$\left(-4, \frac{3 \pi}{4}\right)$$

Consider the following parametric equations. a. Eliminate the parameter to obtain an equation in \(x\) and \(y\). b. Describe the curve and indicate the positive orientation. $$x=5, y=3 t ;-\infty

Use algebraic methods to find as many intersection points of the following curves as possible. Use graphical methods to identify the remaining intersection points. $$r=1-\sin \theta \text { and } r=1+\cos \theta$$