Question

Hello,

I'm working on a problem involving the equation v=sqrt(6*9.8(sin x-0.2 cos x))

Using maxima I have a graph but since maxima uses radians I decided to put sin and cos values multiplied by pi/180 to get degrees.

So I now have a graph which looks roughly right but I'm looking for the angle (x in the equation) which gives the answer v=5 now looking at the graph I have it's come up as 26 but plugging that value into the equation yields and answer other than 5 (5 appears to be the answer when x=35) so that means my graph is incorrect. Anyone got any ideas where I'm going wrong, I think it's the handling of radians and degrees by myself rather than maxima.

Answer 1

I assume Maxima is some application which I don't have, so by the "good ol' fashioned way" ...

5 = √(6*9.8(sin x-0.2 cos x))
square both sides
25 = 6*9.8(sinx - .2cosx)
.42517.. = sinx - .2cosx
.2cosx = sinx - .42517
square again:
.04cos^2 x = sin^2 x - .85034sinx + .18077
.04(1 - sin^2 x) = sin^2 x - .85034sinx + .18077
0 = 1.04sin^2 x - .85034sinx + .14077
using the formula:
sinx = (.85034v ± √.13745)/2.08
= appr .5871 or .23056

<b>x = .62744 or x = .23265</b>

checking the first one:
x = .62744
v = √(6*9.8(sin.62744 - .2cos.62744)
= 4.999991039

not bad I would say.

Answer 2

Hi Reiny, sorry maxima is a computer algebra program that I use. I think my problem stems from the fact maxima takes angles in radians so I think I've probably got myself confused when trying to ensure the program is converting. Thank you for your help.