Question

Determine two pairs of polar coordinates for the point (2, -2) with 0° ≤ θ < 360°.

Answer 1

Is it (2 square root of 2, 135°), (-2 square root of 2, 315°)?

Answer 2

[let x=rcos theta ,y =r sin theta ]
\[2=r \cos \theta ,-2=r \sin \theta \]
square and add
\[4+4=r ^{2}\left( \cos ^{2}\theta+\sin ^{2}\theta \right),r ^{2}=8,r=2\sqrt{2}\]
divide
\[\tan \theta =-1=-\tan \frac{ \pi }{4 }=\tan \left( \pi-\frac{ \pi }{4 } \right),\tan \left( 2\pi-\frac{ \pi }{4 } \right)\]
\[\theta=\frac{ 3\pi }{4 }=135 and \theta=\frac{ 7\pi }{4 }=315\]
polar co-ordinates are
\[(2\sqrt{2},135) and (2\sqrt{2},315)\]

Answer 3

r is always positive.

Answer 4

Well it says one has to be negative.

Answer 5

Thanks btw

Answer 6

(2,-2) are Cartesian co-ordinates.

Answer 7

yw