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What is 7pi in degrees?

3 Answers

Alan P. · Steve J.

Jun 26, 2018

$7 π radians = 1260^{\circ}$ $7pi" radians" = color(blue)(1260^circ)$

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 ( $C$ $C$ ) is related to the radius ( $r$ $r$ ) by the formula
$XXX C = π 2 r$ $color(white)("XXX")C=pi2r$
$XXXXXXXX \Rightarrow$ $color(white)("XXXXXXXX")rArr$ a single radian = $\frac{C}{r} = 2 π$ $C/r=2pi$

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

Relating these two, we have
$XXX 2 π (radians) = 360^{\circ}$ $color(white)("XXX")2pi ("radians") = 360^circ$
or
$XXX π (radians) = 180^{\circ}$ $color(white)("XXX")pi ("radians") =180^circ$

Therefore
$XXX 7 π (radians) = 7 \times 180^{\circ} = 1260^{\circ}$ $color(white)("XXX")7pi ("radians")=7xx180^circ=1260^circ$

Jun 26, 2018

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

Explanation:

$7 π \cdot \frac{180^{\circ}}{π}$ $7pi*180^@/pi$
$(7cancel(pi)180^@)/cancel(pi)$
$7*180^@=1260^@$

Jun 26, 2018

$1260^@$

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!

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