Simultaneous equations Watch

Elbonian
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#1
Report Thread starter 7 years ago
#1
How do I solve the following?

x(0)=A\sin{x}=0.5
\dot{x}(0)=5.3223A\cos{x}=0.1

For x and A

I've worked out the following for the second equation:

A\cos{x}=0.01878887

But I don't know where to go from there. From wolframalpha, I've found the following results: (let b = A and x=x)



I'm expected to find one solution for each, another reason why I'm a little confused because there seem to be multiple solutions from Wolframalpha.

Help would be greatly appreciated.
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Miss Mary
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#2
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#2
If you square both equations
A^2sin^2(x)=0.5^2
A^2cos^2(x)=0.01878887^2
and now you add them
A^2sin^2(x)+A^2cos^2(x)=0.5^2+0.  01878887^2
A^2=0.5^2+0.01878887^2
A=0.500

Now you plug in this value into one of the original equations and work out the value for x.
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ghostwalker
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#3
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(Original post by Elbonian)
...
Help would be greatly appreciated.
Well sin and cos are both periodic functions with a period of 2\pi

And what's 2\pi as a decimal?
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Elbonian
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#4
Report Thread starter 7 years ago
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(Original post by Miss Mary)
If you square both equations
A^2sin^2(x)=0.5^2
A^2cos^2(x)=0.01878887^2
and now you add them
A^2sin^2(x)+A^2cos^2(x)=0.5^2+0.  01878887^2
A^2=0.5^2+0.01878887^2
A=0.500

Now you plug in this value into one of the original equations and work out the value for x.
Ah brilliant, thanks.
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Sternumator
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#5
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I think you can also divide one by the other to get a tanx and the As will cancel
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Elbonian
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#6
Report Thread starter 7 years ago
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(Original post by Sternumator)
I think you can also divide one by the other to get a tanx and the As will cancel
I realized that as well, but thanks.
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