Question

convert these rectangular coordinates to polar coordinates: (-4,3)

Answer 1

\(\large{ \begin{array}{cccllll}
(&-4,&\quad 3)\\
&\uparrow &\uparrow \\
&x&y
\end{array}
\\ \quad \\

r^2=x^2+y^2\implies {\color{brown}{ r}}=\sqrt{x^2+y^2}
\\ \quad \\
tan(\theta)=\cfrac{y}{x}\to tan^{-1}[tan(\theta)]=tan^{-1}\left(\cfrac{y}{x}\right)\to {\color{brown}{ \theta}}=tan^{-1}\left(\cfrac{y}{x}\right)
\\ \quad \\
(\square ,\square )\implies ({\color{brown}{ r}},{\color{brown}{ \theta}})
}\)

Answer 2

(5,-36.86) ?