Polar and Parametric Equations Review

Polar and Parametric Equations Review

Draw

Graph the point $$A\left(2,\frac{5\pi}{3}\right)$$  

Multiple Choice

When r is negative, graph the point...  

• $$\left(-r,\theta+\pi\right)$$  

• $$\left(r,-\theta\right)$$  

• $$\left(\frac{r}{\theta}+\pi,-\frac{\theta}{\pi}\right)$$  

• $$\left(-r,-\theta\right)$$  

Draw

Graph the point $$B\left(-1.5,\frac{5\pi}{6}\right)$$  

Naming Polar Coordinates

Multiple Select

Choose ALL pairs of polar coordinate that also name the point $$\left(3,\frac{7\pi}{6}\right)$$  

• $$\left(-3,\frac{\pi}{6}\right)$$  

• $$\left(-3,-\frac{11\pi}{6}\right)$$  

•    $$\left(3,-\frac{5\pi}{6}\right)$$  

•   $$\left(3,-\frac{\pi}{6}\right)$$  

•   $$\left(-3,\frac{5\pi}{6}\right)$$  

Fill in the Blank

Use your graphic organizer to classify the polar curve $$r=2\cos\theta$$  

Fill in the Blank

Use your graphic organizer to classify the polar curve $$r=2\sin4\theta$$  

Fill in the Blank

Use your graphic organizer to classify the polar curve $$r^2=3^2\cos2\theta$$  

Fill in the Blank

Use your graphic organizer to classify the polar curve $$r=8+4\cos\theta$$   

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Converting Polar Rectangular

USE UNIT CIRCLE

DO NOT ROUND UNLESS NECESSARY​

Multiple Choice

Convert $$\left(-6,\frac{3\pi}{4}\right)$$  into a rectangular coordinate.

• $$\left(-3\ \sqrt[]{2},-3\ \sqrt[]{2}\right)$$  

• $$\left(-3\ \sqrt[]{2},3\ \sqrt[]{2}\right)$$   

• $$\left(3\ \sqrt[]{2},3\ \sqrt[]{2}\right)$$  

• $$\left(3\ \sqrt[]{2},-3\ \sqrt[]{2}\right)$$  

Multiple Choice

Convert $$\left(4,\frac{4\pi}{3}\right)$$  into a rectangular coordinate.

•   $$\left(2,-2\ \sqrt[]{3}\right)$$  

•    $$\left(2,2\ \sqrt[]{3}\right)$$  

•   $$\left(-2,-2\ \sqrt[]{3}\right)$$  

•   $$\left(-2,2\ \sqrt[]{3}\right)$$  

Rectangular Polar

​FIND QUADRANT FIRST AND MATCH WITH UNIT CIRCLE

DO NOT ROUND UNLESS NECESSARY

Multiple Select

Convert $$\left(\frac{\sqrt[]{3}}{2},\frac{1}{2}\right)$$  to polar coordinates. Select two correct answers

• $$\left(1,\frac{\pi}{6}\right)$$  

• $$\left(-1,\frac{7\pi}{6}\right)$$  

• $$\left(-1,-\frac{\pi}{6}\right)$$  

• $$\left(1,-\frac{7\pi}{6}\right)$$  

Parametric Equations

Multiple Choice

Given $$x=5t\$$  and $$y=\sqrt[]{t}+8$$  find $$\left(x,y\right)$$   when $$t=4$$  

• $$\left(\frac{5}{4},12\right)$$  

• (20,10)

• $$\left(20,12\right)$$  

• $$\left(4,8\right)$$  

Parametric Equations in Rectangular Form

1. ​Solve one parametric equation for t.

2. ​Substitute into other parametric equation and solve for y

Multiple Choice

Choose the correct parametric equation written in rectangular form if $$x=t+5\ ,\ y=2t+1$$  

• $$y=2x-11$$  

• $$y=-2x+9$$  

• $$y=2x+11$$  

• $$y=2x-9$$