We say that (r, 0) are polar coordinates for x = (x, y) ER if (x, y) = T . (cos 0, sin 0) = (r cos 0, r sin 0). To distinguish the polar and the Cartesian (or rectangular) coordinates (x, y) of x we write x = (1, y) = pc(r, 0). (x,y) = r(cosee, + sinoe2) e2=(0, 1) coste, + sinoe2 sino e2 cos 0 e, e, =(1,0) 1. Thus, if r 2 0, then r is the distance of x from the origin, and 2. 0 is the angle which the vector x makes with the positive x-direction (in the counterclockwise direction). Exercises Convert the polar coordinates below into rectangular coordinates. (3, ",#) are polar coordinates for ( (8, 2x ) are polar coordinates for ( (-7, # ) are polar coordinates for ( Write x^y for a" Write x*y for a . y (* is required) Write sqrt(z) for V (parenthesis are required) Write pi for IT Check