Question

Find an expression for the length of an arc subtended by each of the following angles in a circle of radius r.



a. 60° b. 270° c. –90°

Answer 1

I think we need a figure

Answer 2

there isnt one :(

Answer 3

OK. So I assume you are talking about angles measured at the origin of the circle, rather than formed on the edge of the circle.

Answer 4

\[\theta = x\]

Answer 5

hold on

Answer 6

now that we know how to calculate the circumference of a circle, we can also calculate the length of an arc (which is simply a portion of the circumference). An angle α defined by two radii subtends an arc. Let's take a look at several examples, from which we can identify a pattern. The arc K in each case is shown as a bold curve. The circumference of the circle is C.

Answer 7

k=1/4 C

Answer 8

SO T thats a quarter of 360

Answer 9

OK
so the circumference C = 2 pi r
for an angle x
the fraction f of 360 degrees is x/360
the formula for the arc length L
L = (x/360) 2 pi r

Answer 10

For the example you are talking about, arc length (k)
k = 1/4 C = (1/4) 2 pi r.
what is r?

Answer 11

so plug in the 60 in plac of the x

Answer 12

Yes

Answer 13

radius

Answer 14

so it would l=60/360*2

Answer 15

it would be 60/360 times 2 pi r

Answer 16

right sorry th

Answer 17

right sorry th

Answer 18

right sorry th

Answer 19

right sorry th

Answer 20

L

Answer 21

for an angle of 60.

for an angle of 90, it would be
90/360 times 2 pi r

Answer 22

my answer is a fraction right

Answer 23

yes, if they didn't give you a value for r

Answer 24

got it U are awESOME

Answer 25

ty

Answer 26

@telliott99 ONe first ?? it was 2188 did u round it off to 22