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

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

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Answer 1 · 2017-02-12T17:31:25

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

Explanation:

Consider what radians are.

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

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

So that means, $360^{o} = 2 π^{c} l$ $360^o=2pi^cl$
I'm using a " $l$ $l$ " 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 $l = \frac{360^{o}}{2 π^{c}}$ $l=360^o/{2pi^c$

Now, we need to find the value of radians for a $1400^{o}$ $1400^o$ . Let's say we already found that it equals this $x^{c}$ $x^c$ (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 $1400^{o} = x^{c} l$ $1400^o=x^cl$ , which can be re-written as $l = \frac{1400^{o}}{x^{c}}$ $l=1400^o/{x^c}$

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

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

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

Now, this is the number of radians we have. We're asked to say how many $π$ $pi$ '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 $x^{c}$ $x^c$ we got with $π$ $pi$ people (of course $π$ $pi$ people can't exist. Three people? yes, 3.1415 people? That'd be interesting)

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

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

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