Taylor's 12th (I think XD) Blog

These are the other half of my notes on Chapter 11.1.

We will be learning how to convert rectangular to polar.

Here are the formulas.

r= square root of x^2 + y^2 tan theta= y/x

polar is in (r,theta) form and rectangular is in (x,y) form.


Now let's work on some problems.
C
onvert (8,9) to polar.

r= square root of 8^2 + 9^2 tan theta= 9/8 First, write out your problem so that
it will match the formula that I gave you.

r= square root of 64 + 81 theta= tan^-1 (9/8) Then for the first part of the equation you square the two numbers. Then for the second part set up the tan so that you are finding the inverse of the fraction.

r= square root of 145 theta= 48.366 degrees Then for the first part of the equation you add the square roots and for the second part you will find the inverse and you will get what I have after you round to the 3rd place after the decimal.
Since you cannot find the square root of 145 you will leave this as your answer and since I cannot use a graph to show you, you need to visualize the quadrant plane for tan and since it is positive we will be using the first and third quadrant. So to get 48.366 degrees to quadrant three you would add 180 degrees and get 228.366 degrees as the answer.

So your answer for this question should look like this (square root of 145 , 48.366 degrees ) and ( - square root of 145 , 228.366 degrees).

Convert (10,12) to polar.

r= square root of 10^2 + 12^2 tan theta= 12/10 First, write out your problem so that it will match the formula that I gave you.

r= square root of 100 + 144 theta= tan^-1 (12/10) Then for the first part of the equation you square the two numbers. Then for the second part set up the tan so that you are finding the inverse of the fraction.

r= square root of 244 theta= 50.194 degrees Then for the first part of the equation you add the square roots and for the second part you will find the inverse and you will get what I have after you round to the 3rd place after the decimal.
Since you cannot find the square root of 145 you will factor out the four and get 2 square root of 61 and since I cannot use a graph to show you, you need to visualize the quadrant plane for tan and since it is positive we will be using the first and third quadrant. So to get 50.194 degrees to quadrant three you would add 180 degrees and get 230.194 degrees as the answer.

So your answer for this question should look like this ( 2 square root of 61, 50.194 degrees ) and ( - 2 square root of 61, 230.194 degrees).

That is the last half of my notes from Chapter 11.1.

SO UNTIL NEXT TIME JA NE!!!!! (Japanese for goodbye.)