Question

Convert the rectangular coordinates (-sqrt2,1) into polar coordinates. I need this please

Answer 1

something noteworthy is that, our x-coordinate is negative whilst the y-coordinate is positive, now, that only occurs on the II Quadrant.

`(\stackrel{ a }{-√(2)}~~,~~\stackrel{ b }{1})\hspace{5em} \begin{cases} r=√(a^2+b^2)\\\\ \theta =\tan^(-1)\left( (b)/(a) \right) \end{cases} \\\\[-0.35em] ~\dotfill`

`r=\sqrt{(-√(2))^2 + (1)^2}\implies r=√(2+1)\implies r=√(3) \\\\\\ \theta =\tan^(-1)\left( \cfrac{1}{-√(2)} \right)\implies \theta =\tan^(-1)\left(-\cfrac{√(2)}{2} \right)\implies \stackrel{ \textit{II Quadrant} }{\theta \approx 144.74^o} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill~ {\Large \begin{array}{llll} \left(√(3)~~,~~144.74^o \right) \end{array}}~\hfill~`