12.06 Graphing polar equations
When we have graphed rectangular equations in the past, we started by creating a table of values. We then plotted the points from the table and connected them with a continuous curve. We can approach graphing polar equations in the same way. This starts with understanding their coordinates and is best seen by looking at some examples.
Practice questions
QUESTION 1
Consider the point $\left(8,\frac{11\pi}{6}\right)$(8,11π6), in polar coordinates.
This point is $\editable{}$ units away from the pole on a polar grid.
What is the size of the angle that the point makes with the polar axis? Give your answer in radians.
Which of the following shows the location of $\left(8,\frac{11\pi}{6}\right)$(8,11π6) on a polar grid?
A polar coordinate grid with several blue points labeled from A to H. The grid has concentric circles increasing in radius at consistent intervals which represents the axes of the polar coordinate grid. The fifth circle is labeled $10$10 indicating that it is the 10th axis. Point $A$A is at $\left(8,\frac{\pi}{3}\right)$(8,π3); point $B$B is at $\left(8,\frac{\pi}{6}\right)$(8,π6); point $C$C is at $\left(8,\frac{11\pi}{6}\right)$(8,11π6); point $D$D is at $\left(8,\frac{5\pi}{3}\right)$(8,5π3); point $E$E is at $\left(4,\frac{\pi}{3}\right)$(4,π3); point $F$F is at $\left(4,\frac{\pi}{6}\right)$(4,π6); point $G$G is at $\left(4,\frac{11\pi}{6}\right)$(4,11π6); point $H$H is at $\left(4,\frac{5\pi}{3}\right)$(4,5π3). The coordinates of all points are not explicitly given in the image and should never be given as answer to any questions/prompts.
QUESTION 2
Convert the point $\left(9,5\right)$(9,5) from rectangular coordinates to polar coordinates $\left(r,\theta\right)$(r,θ), where $0\le\theta<2\pi$0≤θ<2π. Give each value correct to two decimal places.
QUESTION 3
Convert the point $\left(4,\left(-46\right)^\circ\right)$(4,(−46)°) from polar coordinates to rectangular coordinates $\left(x,y\right)$(x,y). Give each value correct to two decimal places.