Now that you have some understanding of converting single points between polar and rectangular form, we are going to move to the next step which is changing equations back and forth between polar and rectangular form.
You already have the notes and homework answer keys from the previous posts. Below are additional notes and links to some videos that demonstrate some examples. Please email me or send me a text if you have questions. I would like to give an assessment by the end of this week. Essentially you are doing identities where you are converting the trig into polar form of an equation or vice versa. To convert from polar to rectangular you want to get rid of all the r's and theta's in the equation and change to terms of x and y. To summarize: There are three main types of techniques as listed below to convert between polar and rectangular forms: 1) You can multiply both sides by r to get: r squared - converts to x squared + y squared or to get: r cos theta - converts to x or to get: r sin theta - converts to y 2) Sometimes you only have r on 1 side of the equation and you don't want to multiply r to the other side because it is already in x and y terms. In this case, SQUARE both sides of the equation so that one side becomes r squared which is now = x squared + y squared. The other side is already in x and y terms, but now squared. So it is still in rectangular form. 3) If you have a theta by itself on one side, take the tangent of both sides of the equation. Tan(theta) = Tan(right side) Since tan x = sin x/cos x (Identity), which is exactly the same as r sin x / r cos x, the left side can now be written as y/x. Then finish the algebra to solve the equation. Some helpful videos. Graphing polar equations in the TI 84 https://www.youtube.com/watch?v=PZwiiZQhM0c&feature=youtu.be Example of a conversion from rectangular (circle) to polar form. https://www.youtube.com/watch?v=tUH6tUiJbH8&feature=youtu.be Example converting a parabola in rectangular form to polar form. https://www.youtube.com/watch?v=XkZAtV8jNb4&feature=youtu.be Video showing how to convert equations from polar back to rectangular coordinates form. https://www.youtube.com/watch?v=IKbRiU7kL2w Email me with your questions.
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