11-1

this is a review from the first section of chapter one. this is converting rectangular to polar and polar to rectangular. to convert rectangular to polar the do [r =(the square root of) x^2 + y^2] then you do [ (tan inverse) y/x]. to go from polar to rectangular you do [x= (r cos (theta) ) and y= r sin (theta) ]. its really easy so lets get an example going.




EX: give polar coordinates (-2,2)
 first r= (the square root of) 2^2 +2^2
you get (square root of) 8 = 2 (square root of) 2
second is (tan inverse) 2/-2 = (tan inverse) -1= 45 (degrees)
tan is -ve in 2nd and 4th quadrant so its is 135 and 315
-2,2 is in Q2 which is where 135 is
answer is [2(square root of) 2, 135 (degrees)] and [-2 (square root of) 2, 315 (degrees)]


give rectangular coordinates (4,120(degrees) )
first x=4 cos 120 and y=4 sin 120
4(-.5)= -2        4(square root of) 3 / 2 = 2 (square root of) 3
answer is (2, 2(square root of) 3)