How do I find the curved length of one complete cycle of the graph of y=cos(x)? I have no clue where to begin. :/
How do I find the curved length of one complete cycle of the graph of y=cos(x)? I have no clue where to begin. :/
@Mathematics

Question

How do I find the curved length of one complete cycle of the graph of y=cos(x)? I have no clue where to begin. :/
 How do I find the curved length of one complete cycle of the graph of y=cos(x)? I have no clue where to begin. :/
 @Mathematics

amistre64 · Answer

iw as thinking it was 2pi, but thats not it is it .... thats the period of cos(x)

amistre64 · Answer

$$ds=\sqrt{dx^2+dy^2}$$ is the basic set up for the integral of a curve

amistre64 · Answer

hmmm, i think you just integrate that .... from 0 to 2pi

amistre64 · Answer

$$\int_{0}^{2pi}\sqrt{1+sin^2(x)}\ dx$$
maybe

anonymous · Answer

well if you graph it, you would see the length = 2pi

amistre64 · Answer

the circumference of the unti circle is 2pi; but i dont think the length of the cos(x) curve is 2pi

anonymous · Answer

you are talking about one cycle of the graph or a period i believe

anonymous · Answer

1 period of that graph is 2 pi

anonymous · Answer

unless you change the length of the perion by going y=2cosx or something like that it would be 2 pi

myininaya · Answer

from x=0 to x=2pi

anonymous · Answer

well i was talk in calc this semester that the length would = 1 period which would be 2 pi

anonymous · Answer

a complete cycle equals 1 complete positive and negative

myininaya · Answer

the length of the interval from x=0 to x=2pi is 2pi
we are looking for the length of curve on that interval

anonymous · Answer

which is a period. guess he would have to look at the book and see which they are looking for

amistre64 · Answer

the length of the curve would have to be greater than 2pi; since 2pi is the linear distance from the origin; and the curve, by nature of being other than linear; would be greater

amistre64 · Answer

period is not the length of the curve, but is the time that it takes for the curve to complete one cycle

anonymous · Answer

amistre has the right formula for arc length at the top.

myininaya · Answer

and i have the right answer :)

amistre64 · Answer

|dw:1321412075493:dw|

anonymous · Answer

right right :)

myininaya · Answer

amistre always gets credit first :(

anonymous · Answer

no wait, isnt what you have just the area under the curve?

myininaya · Answer

no

anonymous · Answer

AH! i see it, my bad.

amistre64 · Answer

$$sin^2 + cos^2 = 1$$
$$sin^2  = 1-cos^2$$

myininaya · Answer

stupid minus sign