# How do you convert (-8,0) into polar forms?

May 5, 2018

$\left(8 , \pi\right)$ (radians) or $\left(8 , {180}^{\circ}\right)$ (degrees)

#### Explanation:

Rectangular $\to$ Polar: $\left(x , y\right) \to \left(r , \theta\right)$

• Find $r$ (radius) using $r = \sqrt{{x}^{2} + {y}^{2}}$
• Find $\theta$ by finding the reference angle: $\tan \theta = \frac{y}{x}$ and use this to find the angle in the correct quadrant

$r = \sqrt{{\left(- 8\right)}^{2} + {\left(0\right)}^{2}}$

$r = \sqrt{64}$

$r = 8$

Now we find the value of $\theta$ using $\tan \theta = \frac{y}{x}$.

$\tan \theta = \frac{0}{-} 8$

$\tan \theta = 0$

$\theta = {\tan}^{-} 1 \left(0\right)$

$\theta = 0 \mathmr{and} \pi$

To determine which one it is, we have to look at our coordinate $\left(- 8 , 0\right)$. First, let's graph it:

As you can see, it is on the negative side of the $x$ axis. Our $\theta$ has to match where that is, meaning that $\theta = \pi$.

From $r$ and $\theta$, we can write our polar coordinate:
$\left(8 , \pi\right)$ (radians) or $\left(8 , {180}^{\circ}\right)$ (degrees)

Hope this helps!