Question

Determine two pairs of polar coordinates for the point (3, -3) with 0° ≤ θ < 360°.

Answer 1

PLEASE

Answer 2

\[Let 3=r \cos \theta ,-3=r \sin \theta \]
square and add,
\[r ^{2}\left( \cos ^{2}\theta+\iota \sin ^{2}\theta \right)=3^{2}+\left( -3 \right)^{2}\]
\[r ^{2}=18=2*9^{2} ,r=3\sqrt{2}\]
\[\frac{ r \sin \theta }{ r \cos \theta }=\frac{ -3 }{ 3 }=-1\]
\[\tan \theta=-1=-\tan \frac{ \pi }{4 }=\tan \left( pi -\frac{ \pi }{4 } \right),\tan \left( 2\pi-\frac{ \pi }{ 4 } \right)\]
\[\theta=\frac{ 3\pi }{4 },\frac{ 7\pi }{ 4 }\]
\[Polar co-ordinates are \left( 3\sqrt{2},\frac{ 3\pi }{4 } \right) and \left( 3\sqrt{2},\frac{ 7\pi }{4 } \right)\]