Question

determine the measure of 0 in radian and degree measures. so length = 8cm, and radius= 5 cm

Answer 1

Given the radius 5 cm, what's the circumference?

Answer 2

um im not sure, would it be 15.75?

Answer 3

no, it's pi times diameter (not pi times radius)

Answer 4

so 31.5 ?

Answer 5

yes or just 10pi

Answer 6

what fraction of the circle is 8 cm (compared to 10pi or 31.5 cm)?

Answer 7

um quater? so 31.5/8? 3.93?

Answer 8

you have it flipped the wrong way

Answer 9

it should be 8/31.5 = 0.25396825, which is roughly a quarter, yes

Answer 10

okay and then what shall I do?

Answer 11

so what you do is you multiply 0.25396825 with 2pi (since one full revolution is 2pi radians)

so the angle in radians is 0.25396825 * 2pi = 1.595729577 radians (this is an approximation)

Answer 12

It turns out that you can also use the idea that

L = theta*r

where L is the arc length and theta is the angle in radians, so...

L = theta*r

8 = theta*5

8/5 = theta

theta = 8/5

theta = 1.6 radians (which is the exact angle in radians)

Answer 13

notice how 1.595729577 is very very close to 1.6

Answer 14

oh yes yes and then how would I get the degree meeasure?

Answer 15

multiply this with 180/pi to convert to degrees

Answer 16

Degree Measure = (1.6)*(180/pi) = ???

Answer 17

91.7 :) wow thank you so much !

Answer 18

you got it