Question

sqrt(-cos(t)+cos(t)+1) = sqrt(2)???

Answer 1

-cos(t)+cos(t)+1 = 1
hence
sqrt(-cos(t)+cos(t)+1) = sqrt(1) = 1

Answer 2

er my bad 1 sec

Answer 3

\[\sqrt{-\sin(t) + \cos(t) + 1}\]

Answer 4

typed wrong thing in

Answer 5

It's not hard to convince yourself that this is not a constant. For example, when x = 0, this is sqrt(2). But when x = pi/4, it is 1.

Answer 6

yeah, no that's what i mean. i'm doing arc length and curvature in cal 3, but the book has an example problem that went from that equation = sqrt(2) with no bounds

Answer 7

When you've figured out your question, post it again.

Answer 8

here
i'll post pic real fast

Answer 9

and how did it go from 2pi to just pi

Answer 10

Oh, it's written incorrectly. It should by sqrt( (-cos t)^2 + (sin t)^2 +1 ) = sqrt(1 + 1) = sqrt(2)

Answer 11

see that's what i was thinking bc it would be the regular distance formula but the book has the formula for this written as.. 1 sec posting

Answer 12

and it should be the integral 0 to 2pi, as the final answer suggests.

But that's a lot of typos in a solution set, and a criminally large number of types for just one problem.

Answer 13

...number of typos ...

Answer 14

yeah hate how this book just skips steps without justifying anything

Answer 15

Also wrong, because it's missing the ^2, the squares of all those derivatives.

Answer 16

wtf ahah

Answer 17

that's what i was thinking.. 1 sec gonna double check online real fast

Answer 18

yeh even patrickjmt on youtube has the squares in it

Answer 19

I have no idea who/what patrickjmt is, but ok.