Due 4/9/20 Polar equations - 1) page. 587 -(problem pages listed on previous post - NOT IN TEXTBOOK). Problem numbers 42-54 evens and number 58 2) Also look at page 594 on the problem page file. It lists the general shapes and generic form of equations for various polar curves. Practice plotting some of the equations and try changing around the values for a, b and r in the different equations to see the effect on the graphs in your calculator. Graph problems 1-6 at the bottom of page 594 - Exercises section 8.2. Make sure you have the proper settings on your calculator, radian, polar, etc. Be aware of the settings of your maximum and minimum x and y values on your calculator as well. See the video below. 3) If you have not already done so, take the "quiz" that was assigned by posting on the link below. https://sites.google.com/sachem.edu/mr-ks-math-and-computer-land/math-12-precalculus The last question on the quiz is to enter the period for your class. While it is now late, you will get some credit it it is taken by the end of tomorrow. Attached below are the notes for this section, the answer key to the homework on page 587 and some links that demonstrate several examples of converting equations between polar and rectangular as well as how to graph an equation in polar form on your TI-84. Read the notes and look at the video examples first. Some review: Video showing how to convert from (x,y) rectangular coordinates to the equivalent in polar coordinates (r, theta). https://www.youtube.com/watch?v=Vg88CWOlDTY 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 Extra notes: Essentially you are doing identities where you are converting the trig into polar form 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. Email me with your questions.
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