11-1 Polar

So this week, I am going to explain how to work Polar Problems. At least I think thats what they are called. So now I am going to give you a few formulas.

To convert from polar to rectangular, you need to know two fomulars. These formulas are:

1. x=r cos theta
2. y=r sin theta

To convert from rectangular to polar, you need to also know two formulas. These formulas are:

1. r= square root of x^2 + y^2
2. theta= tan -1 (y/x)

NOTE: Always graph using the angle (r, theta) instead od (x,y). That is VERY important.

So, now I am going to work a few examples for you.

Example 1: Plot points (2, 40 degrees)

• Since, I can't really explain this in much detail. I am just going to show you a picture of what those points would look like once you plot them and that is going to be your answer.

Example 2: Give the rectangular coordinate for (1, 20 degrees)

• This is when you use the formulas I gave you above.
• 1 = r and 20 degrees = theta
• x=1 cos 20
• y=1 sin 20
• Once you plug those into your calculator, you will get (.940, .342). Which is going to be your answer.

Example 3: Graph r=sin theta

• All you do here is plug this formula into your calculator after making sure you set the correct settings.
• NOTE: Make sure you are in radians and polar mode when graphing these types of problems.
• Now, I am just going to show you what the graph is going to look like.

Well, that is it for this weeeeekk. YAYYY!!! Hope I helped :D

--Halie :)