Measure of the central angle of a circle

[lewch45]

Can anyone help with these 2 problems:

The directions are: Find the measure in radians and degrees of the central angle of a circle subtended by the given arc.

(1) r= 7 feet s= 4 feet


(2) r=3 feet 0= 7 pi/2

Any help would be greatly appreciated. Thanks.

 

[stapel]

How did you answer the other arc-length type questions (that you said you're "okay" on) if you aren't familiar with the arc-length formula? (These are just plug-n-chug arc-length-formula questions, which is why I'm confused.)

. . . . .\(\displaystyle \large{s\,=\,\theta r}\)

Where are you stuck in finding \(\displaystyle \theta\)??

Eliz.

 

[Gene]

For the (1) someone should have told you that
s = r*theta.

For (2) if Theta is 7 pi/2 you can solve for s.

To change radians to degrees multiply by
180/pi

 

[lewch45]

I figured out the first one but I'm a little confused on #2. This is what I have so far.

s= 3 x 7 pi/2

I'm not sure how to break this down to radians and degrees.

 

[Gene]

Same as any. Multiply radians by 180/pi. I don't recall if the arc length can go around the circle more than once or if theta has to be between 0 and 2pi (0 and 360°). Sorry. Stapel will probably let us know.

 

[stapel]

I don't recall if the arc length can go around the circle more than once or if theta has to be between 0 and 2pi (0 and 360°). Sorry. Stapel will probably let us know.

I dunno... I been makin' my share of flubs tonight! :wink:

But I think the answer to the question you post depends, to some extent, on the context and on the definition. If you're doing something like "how much distance does the tire cover in x revolutions, given a tire radius of r?", then the angle measure could be viewed, I think, as being more than 360° (assuming x > 1). On the other hand, the graphical introduction to the topic usually does involve portions of a circle, in which case the arc length could be no more than the circumference.

The original poster will need to look in his/her text to determine what sort of answer is expected. But since the given angle measure is greater than 360°, I would assume the former.

Eliz.