The first video below explains how to map a point on a polar coordinate grid instead of the usual (x,y) Cartesian coordinate system we normally use. The format is (r,theta) theta = the angle
Where r represents how far out from the center pole you are (distance) and theta is the angle you are moving away from the central pole (distance at pole itself is r = 0) https://www.youtube.com/watch?v=-tZR3ggdoIU The next video shows how to give different equivalent representations in polar form for the same exact point. https://www.youtube.com/watch?v=ds-YLa7Yd0k The next video below gives some examples of polar and rectangular coordinates being graphed. https://www.youtube.com/watch?v=A-AEuohaP4o The next video shows how to convert from (x,y) rectangular coordinates to the equivalent in polar coordinates (r, theta). https://www.youtube.com/watch?v=Vg88CWOlDTY The next video shows how to convert from polar coordinates( r, theta) back to rectangular coordinates (x,y). https://www.youtube.com/watch?v=Txx9rvLnuTA Note that polar form is really just a short form of writing the trig form of a vector. If the trig form of a vector is 5(cos 90i +sin90j) then polar form is written as (5, 90) The 5 is the r and the 90 is the theta. You do distribution to go to (x,y) form. cos 90 = 0, and sin 90 is 1 so trig form of 5(cos90i + sin90j) is exactly the same as polar form of (5,90) = (5x0, 5x1) = (0,5) in rectangular or (x,y) form. To write the rectangular form in polar form. r is found by doing the pythagorean theorem on the x,y values r = the square root of x squared + y squared. theta is found the same way as finding the angle with vectors that 3 step process we talked about 1) sketch the vector, 2) arctan of y/x to find the reference angle 3) put the reference angle into the sketch to find the actual angle.
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