Solve the trigonometric equation involve sin(x), cos(x) and sin(x)cos(x)

[daphnelee-mh]

Homework Statement

I had problem with solving the equation while doing my mechanics homework

How to solve equation : 1226.25cosx - 15000sinxcosx + 7500sinx = 0

Relevant Equations

sin^2 + cos^2 = 1

I can’t get the angle, answer given is x=56.33 , x=9.545. (All steps before the equation are correct.)

 

[BvU]

I can’t get the angle, answer given is x=56.33 , x=9.545.

You mean $\theta = 0.983074$ or $\theta = 56.326^\circ$ . Not sure what the x=9.545 means.

All steps before the equation are correct

Confirmed.
Aren't you in a situation where a numerical answer is adequate ? I don't think an analytical answer is possible.

Side note: LHS of your last equation should be a cotangent.

 

[etotheipi]

I tried letting $u = \cos{\theta}$ and ended up with a quartic in $u$, which my calculator could solve (I think it uses the quartic formula), but I certainly wouldn't have the patience to do that myself!

 

[daphnelee-mh]

You mean $\theta = 0.983074$ or $\theta = 56.326^\circ$ . Not sure what the x=9.545 means.
Confirmed.
Aren't you in a situation where a numerical answer is adequate ? I don't think an analytical answer is possible.

Side note: LHS of your last equation should be a cotangent.

 

[daphnelee-mh]

 

[Buzz Bloom]

Hi daphne:

The following may be of some additional help.

sin 2x = 2 sin x cos x

Regards,
Buzz

 

[BvU]

View attachment 260749

I suppose this is a reply to my

Not sure what the x=9.545 means

And I must humbly admit I discarded the second answer in the wolfram link because it's so far away from the initial 60$^\circ$. But it satisfies the equation.

Is it clear that an analytical solution is unlikely to be found for this problem, so a numerical solution should be acceptable ?