Convert the given rectangular coordinates to polar coordinates. Express the answer in such a way that r is nonnegative and $0 \leq \theta

Question

Convert the given rectangular coordinates to polar coordinates. Express the answer in such a way that r is nonnegative and $0 \leq \theta < 2 \pi$ . $( 7,0 )$
A) $( 0,7 )$
B) $( 7,0 )$
C) $\left( - 7 , \frac { 3 \pi } { 2 } \right)$
D) $( - 7,0 )$
E) $\left( 7 , \frac { 3 \pi } { 2 } \right)$

Quizplus · Accepted Answer

To convert rectangular coordinates to polar coordinates, we use the formulas
\begin{align*}
x &= r \cos 	heta \
y &= r \sin 	heta
\end{align*}
Since the given point is $(7,0)$, we have $x=7$ and $y=0$. This tells us that $r \cos 	heta = 7$ and $r \sin 	heta = 0$. Since $\sin 	heta$ is zero when $	heta$ is an even multiple of $\pi$, we have two possible values for $	heta$: $	heta = 0$ or $	heta = \pi$ (however, we are asked to express $	heta$ in the interval $0 \leq 	heta < 2\pi$, so we choose $	heta = 0$). Solving for $r$, we get $r = \frac{x}{\cos 	heta} = \frac{7}{\cos 0} = 7$. Therefore, the polar coordinates are $(r, 	heta) = (7,0)$.

Convert the Given Rectangular Coordinates to Polar Coordinates 0≤θ<2π0 \leq \theta < 2 \pi0≤θ<2π

Convert the Given Rectangular Coordinates to Polar Coordinates $0 \leq \theta < 2 \pi$