Expert: Paul Klarreich - 7/28/2009

Question
the rectangular coordiantes of a point are given. Find two pairs of polar coordiantes, one with r>0 and one with r<0. Express the angles in radians.

Ok I got everything except the last part, like changing r>0 and r<0.

here is my work :

r= x^2+y^2 whole square root.

= (1)^2 + (-1)^2 whole square root

r= √2

Angle = tan^-1 y/x

= tan^-1 (-1/1)

=-45

=-pi/4

r>0 (√2, -pi/4)

r<o (-√2, -pi/4)

Is that right ? or do i have to chang the -pi/4 too ?? please help ! thanks !!

Answer
Questioner: Pratap
Country: United States
Category: Advanced Math
Private: No
Subject: Rectangular coordinates
Question: the rectangular coordiantes

>> That's "coordinates".  (I make that same typo all the time.)

of a point are given. Find two pairs of polar coordinates, one with r>0 and one with r<0. Express the angles in radians.

Ok I got everything except the last part, like changing r>0 and r<0.

here is my work :

r= x^2+y^2 whole square root.

= (1)^2 + (-1)^2 whole square root

r= √2

Angle = tan^-1 y/x

= tan^-1 (-1/1)

=-45

= -pi/4

r>0 (√2, -pi/4)

r<0 (-√2, -pi/4)

Is that right ? or do i have to chang the -pi/4 too ?? please help ! thanks !!
.......................
Yes, you do.  If the r is <0, you have rotated another 180, or pi.

So you must have:

r>0 (√2, -pi/4)

r<0 (-√2, 3pi/4)