# What is 7pi in degrees?

Jun 26, 2018

$7 \pi \text{ radians} = \textcolor{b l u e}{{1260}^{\circ}}$

#### Explanation:

Background:
The circumference of a circle gives the number of radians (number of segments of length equal to the radius) in the circumference. That is a "radian" is the length of the circumference divided by the length of the radius.

Since the circumference ($C$) is related to the radius ($r$) by the formula
$\textcolor{w h i t e}{\text{XXX}} C = \pi 2 r$
$\textcolor{w h i t e}{\text{XXXXXXXX}} \Rightarrow$ a single radian = $\frac{C}{r} = 2 \pi$

In term of degrees, a circle, by definition, contains ${360}^{\circ}$

Relating these two, we have
$\textcolor{w h i t e}{\text{XXX")2pi ("radians}} = {360}^{\circ}$
or
$\textcolor{w h i t e}{\text{XXX")pi ("radians}} = {180}^{\circ}$

Therefore
$\textcolor{w h i t e}{\text{XXX")7pi ("radians}} = 7 \times {180}^{\circ} = {1260}^{\circ}$

Jun 26, 2018

$\pi = {180}^{\circ}$, so $7 \pi = {1260}^{\circ}$.

#### Explanation:

$7 \pi \cdot {180}^{\circ} / \pi$
$\frac{7 \cancel{\pi} {180}^{\circ}}{\cancel{\pi}}$
$7 \cdot {180}^{\circ} = {1260}^{\circ}$

Jun 26, 2018

${1260}^{\circ}$

#### Explanation:

From our definition of a radian, we know

$\pi$ rad=$\textcolor{b l u e}{{180}^{\circ}}$

To convert $7 \pi$ to degrees, we multiply what's in blue by $7$:

$\textcolor{red}{7} \textcolor{b l u e}{\pi}$ rad=$\textcolor{red}{7} \cdot \textcolor{b l u e}{180} = {1260}^{\circ}$

Therefore, $7 \pi$ rad is equal to ${1260}^{\circ}$.

Hope this helps!