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.
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
x = .62744 or x = .23265
checking the first one:
x = .62744
v = √(6*9.8(sin.62744 - .2cos.62744)
= 4.999991039
not bad I would say.
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.
Hello,
It seems like you are on the right track but may have made some mistakes in converting between radians and degrees. Let's go through the steps and see if we can identify the issue.
1. Start with the equation v = sqrt(6 * 9.8 * (sin x - 0.2 * cos x)). We want to find the value of x that gives v = 5.
2. First, let's convert the angle x from degrees to radians. To do this, multiply x by π/180.
3. Substitute the value of x in radians into the equation and solve for v. In this case, v = 5.
4. Since the equation may be difficult to solve analytically, we can use numerical methods, such as trial and error or using a graphing calculator or software. It seems like you have already used Maxima to graph the equation.
5. Plot the graph and see if there are any points where v equals 5. It's important to ensure that the graph is correctly plotted by using the correct radians or degrees.
6. If the graph does not show v = 5 at x ≈ 26, then there may be an error in your conversions or calculations. Double-check the conversion from degrees to radians to make sure it is accurate. Also, review the equation and calculations to ensure there are no other errors.
7. If you are still unable to find the correct value of x using the graph or any other method, you may need to use more advanced techniques, such as numerical approximation methods like Newton's method or a root-finding algorithm.
It's worth noting that it might be helpful to double-check the units and calculations to make sure everything aligns correctly. Sometimes, a small mistake in calculations or conversions can lead to unexpected results.
I hope this helps you identify the issue and find the correct solution to your problem.