Question

What is 7pi in degrees?

Answer 1

`7pi" radians" = color(blue)(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
`color(white)("XXX")C=pi2r`
`color(white)("XXXXXXXX")rArr` a single radian = `C/r=2pi`

In term of degrees, a circle, by definition, contains `360^circ`

Relating these two, we have
`color(white)("XXX")2pi ("radians") = 360^circ`
or
`color(white)("XXX")pi ("radians") =180^circ`

Therefore
`color(white)("XXX")7pi ("radians")=7xx180^circ=1260^circ`

Answer 2

`pi=180^@`, so `7pi=1260^@`.

Explanation:

`7pi*180^@/pi`
`(7cancel(pi)180^@)/cancel(pi)`
`7*180^@=1260^@`

Answer 3

`1260^@`

Explanation:

From our definition of a radian, we know

`pi` rad=`color(blue)(180^@)`

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

`color(red)7color(blue)(pi)` rad=`color(red)7*color(blue)(180)=1260^@`

Therefore, `7pi` rad is equal to `1260^@`.

Hope this helps!