## Precalculus (6th Edition) Blitzer

The required ordered pair in polar coordinates is $\left( 6,\pi \right)$.
The Cartesian coordinates in the polar form are given by $x=r\,\cos \,\theta \ \ \text{ and }\ y=r\,\sin \,\theta$. The provided data is $x=-6\ \text{ and }\ y=0$. Therefore, we can determine the required polar coordinates by using the following formulas: $r=\sqrt{{{y}^{2}}+{{x}^{2}}}\ \text{ and }\ \text{tan}\,\theta =\frac{y}{x}$ Therefore, the polar coordinate r is given by: \begin{align} & r=\sqrt{{{y}^{2}}+{{x}^{2}}} \\ & =\sqrt{{{\left( -6 \right)}^{2}}+{{0}^{2}}} \\ & =\text{6} \end{align} and \begin{align} & \text{tan}\,\theta =\frac{y}{x} \\ & =\frac{0}{-6} \\ & =0 \end{align} Therefore, $\theta =\pi$. Thus, the required polar coordinates are $\left( r,\theta \right)=\left( 6,\pi \right)$.