A point in rectangular coordinates is given. Convert the point to polar coordinates. $( 4,4 )$
A) Polar coordinates: $\left( \sqrt { 4 } , \frac { \pi } { 4 } \right)$
B) Polar coordinates: $\left( - \sqrt { 4 } , \frac { \pi } { 4 } \right)$
C) Polar coordinates: $\left( 4 \sqrt { 2 } , \frac { \pi } { 4 } \right)$
D) Polar coordinates: $\left( - 4 \sqrt { 2 } , \frac { \pi } { 4 } \right)$
E) Polar coordinates: $\left( 4 \sqrt { 2 } , - \frac { \pi } { 4 } \right)$

Question

A point in rectangular coordinates is given. Convert the point to polar coordinates. $( 4,4 )$ 
A) Polar coordinates: $\left( \sqrt { 4 } , \frac { \pi } { 4 } \right)$
B) Polar coordinates: $\left( - \sqrt { 4 } , \frac { \pi } { 4 } \right)$
C) Polar coordinates: $\left( 4 \sqrt { 2 } , \frac { \pi } { 4 } \right)$
D) Polar coordinates: $\left( - 4 \sqrt { 2 } , \frac { \pi } { 4 } \right)$
E) Polar coordinates: $\left( 4 \sqrt { 2 } , - \frac { \pi } { 4 } \right)$

Quizplus · Accepted Answer

To convert from rectangular coordinates to polar coordinates, we use the formulas:
$$r = \sqrt{x^2+y^2}$$
$$\theta = \tan^{-1}(\frac{y}{x})$$
Plugging in the values $x=4$ and $y=4$, we get:
$$r = \sqrt{4^2+4^2}=\sqrt{32}=4\sqrt{2}$$
$$\theta = \tan^{-1}(\frac{4}{4})=\frac{\pi}{4}$$
Therefore, the polar coordinates of $(4,4)$ is $\boxed{\textbf{(C)}\ (4\sqrt{2},\frac{\pi}{4})}.$

A Point in Rectangular Coordinates Is Given (4,4)( 4,4 )(4,4) A) Polar Coordinates

A Point in Rectangular Coordinates Is Given $( 4,4 )$ A) Polar Coordinates