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

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.)

## Answers and Replies

BvU
Science Advisor
Homework Helper
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
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!

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. Buzz Bloom
Gold Member
Hi daphne:

The following may be of some additional help.

sin 2x = 2 sin x cos x

Regards,
Buzz

BvU
Science Advisor
Homework Helper
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 ? 