Discussion in 'Random Ramblings' started by arabookworm, Nov 22, 2009.

1. ### arabookwormChillin' With My Peeps

Oct 27, 2008
Pittsburgh, PA
two questions. I don't necessarily want them solved for me, I just can't figure out how to get started on them.

1) prove the identity 2arcsinx=arccos(1-2x^2)

2)a rain gutter is to be constructed from a metal sheet 30cm wide by bending up one third on each side to form angle a. what should angle a be in order to maximize the amount of water the gutter can hold?

Last edited: Nov 22, 2009
2. ### arabookwormChillin' With My Peeps

Oct 27, 2008
Pittsburgh, PA

3. ### ImpAll things share the same breath- Chief Seattle

9. Worksheet for Level 4 Problem
Set f(x) = 2 arcsin(x) − arccos(1 − 2x2). Since d
dx (arcsin(x)) = − d
dx (arccos(x)) = p 1
1−x2, we
have
f0(x) = p 2
1 − x2 − (−4x)p −1
1 − (1 − 2x2)2
= p 2
1 − x2 − p 4x
4x2 − 4x4
= p 2
1 − x2 − p 2
1 − x2
= 0
for x > 0, thus f(x) = c for x > 0, for some constant c. Setting x = p1
2 gives f

p1
2

= 2(
4 )−
2 =
0, and as f(0) = 0, 2 arcsin(x) = arccos(1 − 2x2) as asserted.

Yes I know Calculus too.

Imp-Knows nothing about gutters. Hope this helps

Quote:

5. ### NoseyChickensFeathers On The Ground

2,405
15
193
Aug 3, 2009
Southern California
Well, that just made me feel stupid!

6. ### arabookwormChillin' With My Peeps

Oct 27, 2008
Pittsburgh, PA
Quote:so the derivative of arcsinx is -d and the derivative of arccos(1-2x^2) is p1? but what are d and p? I hate identities right now... nope, strike that, I hate them always.

7. ### newchickenfamilyChillin' With My Peeps

Apr 30, 2008
SF Bay Area - Danville
just thinking about calculus makes me want to

8. ### Iowa Roo MomResistance Is Futile

Apr 30, 2009
Keokuk County

9. ### ImpAll things share the same breath- Chief Seattle

Arabookworm,

Sorry I have no idea what any of this means. It has been decades since I've seen calculus. I googled

this---> 2arcsinx=arccos(1-2x^2)

and got lots of hits.

This one seemed closest to what you were looking for----> www.math.siu.edu/mills/Math150Sum2003_ak_exam5_1.pdf

Maybe you could try googling and find the answer you need

Good luck.

Just a guess, but shouldn't the angle on the gutter be the one that maximizes the area in the cut view of the gutter?--> \\_/. Thus maxing the volume of the gutter? I have no idea how to get there.

Imp-Going to lie down now.

10. ### McCord6Away

With Geometry, I would be able to help you but Calculus? Didn't even take it in high school!