SOLUTION: Convert the following cartesian coordinates to polar coordinates using radians. a) (1,0) b) (0,-4) c) (3,-3) d)(-1,2)

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Convert the following cartesian coordinates to polar coordinates using radians. a) (1,0) b) (0,-4) c) (3,-3) d)(-1,2)      Log On


   

Question 1157770: Convert the following cartesian coordinates to polar coordinates using radians.
a) (1,0)
b) (0,-4)
c) (3,-3)
d)(-1,2)
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

a) (1,0)
r=sqrt%28x%5E2%2By%5E2%29
r=sqrt%281%5E2%2B0%5E2%29
r=1
theta+=tan%5E-1+%28y%2Fx%29
theta+=tan%5E-1+%280%2F1%29
theta+=tan%5E-1+%280%29
theta+=0radians

=>the polar coordinates: (1,0)
b) (0,-4)
r=sqrt%28x%5E2%2By%5E2%29
r=sqrt%280%5E2%2B%28-4%29%5E2%29
r=sqrt%2816%29
r=4
theta+=tan%5E-1%28y%2Fx%29
theta+=tan%5E-1%28-4%2F0%29-> undefined
the polar coordinates of (0,+-4 ) is (4, undefined+)

c) (3,-3)
r=sqrt%28x%5E2%2By%5E2%29
r=sqrt%283%5E2%2B%28-3%29%5E2%29
r=sqrt%289%2B9%29
r=sqrt%282%2A9%29
r=3sqrt%282%29
theta+=tan%5E-1+%28y%2Fx%29
theta+=tan%5E-1+%28-3%2F3%29
theta+=tan%5E-1+%28-1%29
theta+=-pi%2F4
the polar coordinates: (3sqrt%282%29, -pi%2F4)

d) (-1,2)
r=sqrt%28x%5E2%2By%5E2%29
r=sqrt%28%28-1%29%5E2%2B2%5E2%29
r=sqrt%281%2B4%29
r=sqrt%285%29
theta+=tan%5E-1+%28y%2Fx%29
theta+=tan%5E-1+%282%2F-1%29
theta+=tan%5E-1+%28-2%29
theta+=-1.107
the polar coordinates: (sqrt%285%29,-1.107)