Question

hey guys, have a ... lets go with "difficult" question:

if x*y = P
and x = a* sin (phi)
and y = b* sin (phi - theta)
and a = 162
and b = 7.5
and theta = 50 degrees

... how do i find the value for P(maximum) ... please?
and also the corresponding value for phi i guess?

Answer 1

hey @tkhunny how u dooin? any ideas on the above dude?

Answer 2

Have you considered substituting everything and finding all the 1st and 2nd partial derivatimes, \(\dfrac{dP}{d\phi}\)?

Answer 3

i did, but then i realised i learned partial derivatives last term, so over the course of 4 months have forgotten how to do them... dammit

Answer 4

know a good refresher site to relearn partial derivatives dude?

Answer 5

We can simply remove the \(\theta\) problem with trig identities.

\(\sin(\phi - \theta) = \sin(\phi)\cos(\theta)-\cos(\phi)\sin(\theta)\)

Answer 6

Actually, there is no PARTIAL derivative problem, here. \(\theta\) is a constant.

Answer 7

https://www.khanacademy.org/math/calculus/partial_derivatives_topic/partial_derivatives/v/partial-derivatives

Answer 8

yup: 50

Answer 9

Okay, we're down to \(\dfrac{d}{d\phi}[1215\sin(\phi)\sin(\phi - 50º)]\). What do you get for that derivative?

Answer 10

https://www.khanacademy.org/math/calculus/partial_derivatives_topic/partial_derivatives/v/partial-derivatives @Jack1

Answer 11

1215 [cos (phi-50) sin(phi)] + cos (phi) sin (phi + 50) ... is that right?

Answer 12

You have some trigonometry to go to make your life easier, unless you're okay with that result. With that correction, It's right, but it's way ugly.

I get \(\dfrac{dP}{d\phi} = 1215\cdot\sin\left(2\phi - \dfrac{5\pi}{18}\right) = 2430\cdot\sin^{2}\left(\phi + \dfrac{\pi}{9}\right) - 1215\)

Kind of remarkable that those are the same.

Answer 13

i dont think im doing it right, the answer's supposedly 1000 Watts @ phi = 115 degrees

cheers anyway @tkhunny for the help, i think i needs more study time to understand the basics before i try for the specifics

Answer 14

k i dont understand how they got it, but one of my mates sent me how he did it (its a 2008 practice exam we're going through):

if y = -1215. sin (50 - x) sin(x) (x is phi)
y' = -1215. sin (50 - 2x)...
he didn't email the explanation, just the result
so 0 = -1215. sin (50 - 2x)
so x = phi = 25 -(pi n /2) = so that'll give me the low and the high points, -65 was a minimum, 115 was a maximum

it seems to be right, (P = 998 Watts) but I clearly don't get the maths (derivatives using product rule then chain rule consecuatively ... or spelling consecuatively...) so will have to work on it whay more.
Thanks again @tkhunny
Jack

Answer 15

You don't recognize one of my derivatives? " y' = -1215. sin (50 - 2x)"