• Jan 13th 2011, 02:02 PM
Mike012
Just got done reading the chapter... Want to make sure I have this right....

IF Circumference = 2(pi)r
Let cir = 360 deg.
So that 360 deg = 2(pi)r

And 180 deg = (pi)r

IF r = 10
then 180 = (pi)10

Hence half of a cirlce with radius of 10 has an arc measure of 10(pi).....

Is this correct?

And if I wanted to find An arc measure of angle 70 deg I would
solve for x
180x = 70
x = 70/180 = 7/18
then
70 = (7/18)(Pi)(10)
• Jan 13th 2011, 02:11 PM
pickslides
Quote:

Originally Posted by Mike012
So that 360 deg = 2(pi)r

One is the measure of degrees inside a circle the other is the length around the circle.

You can say $\displaystyle 360^{\circ} = 2\pi^c$

Or $\displaystyle C= 2\pi r$ when $\displaystyle r=10 \implies C =2\times \pi \times 10 \approx 62.8$
• Jan 13th 2011, 02:22 PM
Mike012
you repeated what I said....
• Jan 13th 2011, 02:33 PM
skeeter
Quote:

Originally Posted by Mike012
you repeated what I said....

you said $\displaystyle 360 = 2\pi r$ ; that is not true.

$\displaystyle 360$ degrees = $\displaystyle 2\pi$ radians ... the radius doesn't matter.

an angle $\displaystyle \theta$ measured in radians is defined as $\displaystyle \displaystyle \theta = \frac{s}{r}$ , where $\displaystyle s$ is the arclength of the intercepted arc.

so, for a whole circle, $\displaystyle \displaystyle \theta = \frac{2\pi r}{r} = 2\pi$
• Jan 13th 2011, 02:37 PM
pickslides
Quote:

Originally Posted by Mike012
And if I wanted to find An arc measure of angle 70 deg I would
solve for x
180x = 70
x = 70/180 = 7/18
then
70 = (7/18)(Pi)(10)

I measure an arc length as $\displaystyle L = \frac{\theta}{360}\times 2\pi r$

In your case, $\displaystyle r=10, \theta = 70 , L = \frac{70}{360}\times 2\pi \times 10=\dots$
• Jan 13th 2011, 02:39 PM
e^(i*pi)
Quote:

Originally Posted by Mike012
Just got done reading the chapter... Want to make sure I have this right....

IF Circumference = 2(pi)r
Let cir = 360 deg.
So that 360 deg = 2(pi)r

And 180 deg = (pi)r

No r comes after the circumference equation since the 1 radian is the angle subtended by an arc of length equal to the radius. If we want to find out how many radians are in a full circle we can divide the circumference by the number of radii - $\displaystyle \theta = \dfrac{C}{r} = \dfrac{2\pi r}{r} = 2\pi$

Then set this equal to 360 degrees to give $\displaystyle \pi rad = 180^{\circ}$

Quote:

IF r = 10
then 180 = (pi)10
No, angle measurement is independent of the radius. $\displaystyle 180^o = \pi$

Quote:

Hence half of a cirlce with radius of 10 has an arc measure of 10(pi).....

Is this correct?
Yes. Arc length = Angle * radius or $\displaystyle l = \theta r$

Quote:

And if I wanted to find An arc measure of angle 70 deg I would
solve for x
180x = 70
x = 70/180 = 7/18
then
70 = (7/18)(Pi)(10)
$\displaystyle 1 degree = \dfrac{\pi}{\180} rad$ so 70 degrees is $\displaystyle \dfrac{7\pi}{18}$ (note I have multiplied by pi when finding the angle)
$\displaystyle l = 10 \cdot \dfrac{7\pi}{18}$