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Anonymous
How to solve this as a function of x? 2016-12-16 05:23:03 Post No. 8543969
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How to solve this as a function of x? 2016-12-16 05:23:03 Post No. 8543969
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I'm working in a project for college and I really need to transform the following equation to make h the variable, as a function of x. Can anyone do this? I'm having trouble because it's not linear.
h = r1 * sin(x) + r2 * sin(2 * x) + r3 * sin(3 * x) + r4 * sin(4 * x) + r5 * sin(5 * x)
x(h) = ?
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it's a periodic function so you'll have to take a restriction to make it injective.
are the r1. r2 etc constants?
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x belongs to ]0; pi/2[ and r1, r2, etc. are constants, yes.
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Use Euler's formula and write the sine terms as complex exponentials, use law of exponents and make a change of variable. It'll really make you think.
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>>8543969
sin(a+b) = sin(a)cos(b) + sin(b)cos(a)
sin^2(x) + cos^2(x) = 1
and use pic-related. Not sure if it'll work if rk =/= r(k+1), but I'm sure it's worth a try
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>>8544046
forgot pic-related
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>>8544028
that might help, thanks
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Not doable.
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>>8543969
Expanding it comes down to solving a degree-10 polynomial. Which requires a numerical solution. So you may as well solve the original equation numerically.
Note that the solution may only be unique over the range [-pi/10,pi/10].
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