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

  • #1

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
2FB72C80-5100-4229-9C9D-A3E77A200E37.jpeg

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

  • #2
BvU
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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## :wink: . 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.
 
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  • #3
etotheipi
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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!
 
  • #4
You mean ##\theta = 0.983074## or ##\theta = 56.326^\circ## :wink: . 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.
 
  • #5
37F42899-18C2-4C37-B719-4ED57A6EE48D.jpeg
 
  • #6
Buzz Bloom
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Hi daphne:

The following may be of some additional help.

sin 2x = 2 sin x cos x

Regards,
Buzz
 
  • #7
BvU
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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 ?
1587590878458.png
 

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