We say that (r, 0) are polar coordinates for x = (x, y) = R if...

Transcribed Image Text:

We say that (r, 0) are polar coordinates for x = (x, y) = R if To distinguish the polar and the Cartesian (or rectangular) coordinates (x,y) of x we write e=(0,1) (x, y) = r. (cos , sin 0) = (r cos , r sin 0). sine e cos e X = = (x, y) = pc(r, 0). (x,y)=r(cosee, + sin0e) cos0e,+ sin0e e=(1,0) 1. Thus, if r > 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. (9,7) are polar coordinates for (6, 5.) are polar coordinates for 3 (-6, 3-T) are polar coordinates for ( Write x^y Write x*y Write sqrt(z) Write pi for xy for xy (* is required) for z (parenthesis are required) for T We say that (r, 0) are polar coordinates for x = (x, y) = R if To distinguish the polar and the Cartesian (or rectangular) coordinates (x,y) of x we write e=(0,1) (x, y) = r. (cos , sin 0) = (r cos , r sin 0). sine e cos e X = = (x, y) = pc(r, 0). (x,y)=r(cosee, + sin0e) cos0e,+ sin0e e=(1,0) 1. Thus, if r > 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. (9,7) are polar coordinates for (6, 5.) are polar coordinates for 3 (-6, 3-T) are polar coordinates for ( Write x^y Write x*y Write sqrt(z) Write pi for xy for xy (* is required) for z (parenthesis are required) for T