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I really need to solve this equation, but my knowledge is not enough to figure it out:

$$\cos(-55.82) = (0.6893\cos(-70) + 0.3381\sin(-70)) \cdot (-\frac{-0.4206\cos f + 0.6423 \sin f}{\sin 67.33}) - (-0.6408(-\frac{(0.0533\cos(-70) + (-0.9057\sin(-70))) \cdot \cos f + 0.6423\sin f}{ \sin 67.33}))$$

I need to solve value of $f$. I would really appreciate some help.

After edit: OK, then I have something like that:

$$0.5618 = -0.0819 \cdot (-\frac{-0.4206\cos f + 0.6423 \sin f}{0.9227}) - (-0.6408(-\frac{0.8693 \cdot \cos f + 0.6423\sin f}{0.9227}))$$

When I enter it into wolfram alpha I get the result: wolfram, but when I enter it into solve, it didn't gave me any reasonable result :/ Do you have any more suggestions? And thanks guys for your help. I have something like that now: $$0.895475 sin(f)+1.00816 cos(f)=0$$

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Replace all the terms which do not involve $f$ by their values. You will end with a linear equation $$A + B \cos (f)+\text{C} \sin (f)=0$$ for which you would not find any analytical solution. What I suggest is that you plot your function and check where it is close to zero. Then, reduce the search interval and again.

Do not forget Wolfram Alpha as suggested by user88595.

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  • $\begingroup$ Actually, you can find an analytical solution: wolframalpha.com/input/… $\endgroup$ – Daniel R Feb 5 '14 at 16:56
  • $\begingroup$ @DanielR. For sure and for loooon time! But, why didn't you enter the values of $a$, $b$ and $c$ ? Since I am almost blind, I was just unable to be sure I typed properly OP's equation. Cheers. $\endgroup$ – Claude Leibovici Feb 5 '14 at 17:01
  • $\begingroup$ Claude, I didn't have the time to deciphre the expression in the OP. I just wanted to make you aware of that there is an analytical solution to the general equation you wrote. I guess I misinterpreted "you would not find" as "there is no". I guess it should read "it will take a long time to find" or "you don't have the guts to find" or something. :) $\endgroup$ – Daniel R Feb 6 '14 at 12:50
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Ok... Most of the expressions are just numbers so just deal with them like you would deal with $-x+1 = 2$ for example.

The hard bit comes because of $\cos f$ and $\sin f$. It is hard to solve exactly because of the randomness of the numbers. There exist numerical packages which will solve this easily. Most maths program (or wolframalpha online) will do so.

Assuming all your numbers have 4 significant figures, therefore are approximations of exact numbers, it does not make sense to look for an exact solution.

Hoping I have correctly copied it (please check!) here are the solutions found using wolframalpha <- (link)

The above result is assuming you have degrees which was a false assumption. Here's the new result still using wolfram with radians.

Result are approximately:

  • $f = -1.17 + 2n\pi$

  • $f = -0.109 + 2n\pi$

$\forall \,n\in \mathbb Z$

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    $\begingroup$ A word of caution: By the looks of the question I would assume that the angles are expressed in degrees, but the Wolfram Alpha result is calculated using radians. $\endgroup$ – Daniel R Feb 5 '14 at 16:22
  • $\begingroup$ Daniel R is correct, I didn't told you that those are degrees, so your equation is not correct, sorry. And thanks for effort. $\endgroup$ – user126448 Feb 5 '14 at 18:20
  • $\begingroup$ ah yes, didn't think about that. Then convert to radians in wolfram! $\endgroup$ – user88595 Feb 6 '14 at 11:50

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