# How do you change 1400 to radian measure in terms of pi?

##### 1 Answer
Feb 12, 2017

${x}^{c} = 7.7777 {\pi}^{c}$

#### Explanation:

Consider what radians are.

A complete circle is said to have $2 \pi$ radians (if anyone asks why then say that it's made to fit the system of unit circles, circumference $c = 2 \pi r$ with $r =$unit means $c = 2 \pi$ making trigonometric equations easier)

Now, a complete circle is also ${360}^{o}$.

So that means, ${360}^{o} = 2 {\pi}^{c} l$
I'm using a "$l$" here because we don't know how exactly they're related, but we know that they're directly related this way.
Rearrange the equation and we get l=360^o/{2pi^c

Now, we need to find the value of radians for a ${1400}^{o}$. Let's say we already found that it equals this ${x}^{c}$ (that "c" on top implies that the number we're talking about here is radians, you might have noticed the "o" on top of the degrees by now)

So that means ${1400}^{o} = {x}^{c} l$, which can be re-written as $l = {1400}^{o} / \left\{{x}^{c}\right\}$

It seems like we got two equations for $l$, so let's equate the two, meaning we get
${1400}^{o} / \left\{{x}^{c}\right\} = {360}^{o} / \left\{2 {\pi}^{c}\right\}$

Rearranging, I get
$\frac{{1400}^{o} \cdot 2 {\pi}^{c}}{360} ^ o = {x}^{c}$

Now, this is why I'm happy calculator exists, which means if you used one here, you'd get ${x}^{c} = {24.43460952792061}^{c}$, or more simply ${x}^{c} = {24.4346}^{c}$

Now, this is the number of radians we have. We're asked to say how many $\pi$'s are there (but not a lot of pies sadly).

Now, if I had three chocolate bars, and had to distribute them among 2 people(excluding me), how many would each person have? Well, each person would have 1.5 chocolate bars.

Same thing here, we'll divide the value of ${x}^{c}$ we got with $\pi$ people (of course $\pi$ people can't exist. Three people? yes, 3.1415 people? That'd be interesting)

That means ${x}^{c} = 7.7777 {\pi}^{c}$