Question

Determine two pairs of polar coordinates for the point (4, 4) with 0° ≤ θ < 360°.
(4 square root 2, 135°), (-4 square root 2, 315°)
(4 square root 2, 45°), (-4 square root 2, 225°)
(4 square root 2, 315°), (-4 square root 2, 135°)
(4 square root 2, 225°), (-4 square root 2, 45°)

Answer 1

\[put~4=r\cos \theta~and~ 4=r \sin \theta\]
square and add
\[16+16=32=r^2\left( \cos ^2\theta+\sin ^2 \theta \right),r^2=32,r=\pm \sqrt{32}\]
as x and y co-ordinates are positive so point lies in first co-ordinate.
divide
\[\frac{ r \sin \theta }{ r \cos \theta }=\frac{ 4 }{ 4 }=1,\tan \theta=1,\theta =45\]
so polar co-ordinates are
(r,theta) and (-r,theta +180)
or
\[(4\sqrt{2},45),(-4,45+180)~or~(4\sqrt{2},45) ~and~(-4,225)\]

Answer 2

So the answer is B? @sshayer

Answer 3

pair of polar co-ordinates are=\[\left( r,\theta \right) and \left( -r,\theta \pm \pi \right)\]
second option is correct.

Answer 4

Thank you

Answer 5

yw