Solving simple symbolic trigonometry equations

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John 2016-1-28

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评论： John 2016-2-2

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I have a simple trigonometric equation I would like to solve, but I can't seem to get Matlab to give me an answer:

a*sin(x)-b*cos(x) = 0

I want to solve for x. This has a trivial solution and is easy to see by eye:

x = atan(b/a) and x = atan(b/a) + pi

I'd like to know whether it's possible to lead Matlab to the answer. I've tried:

syms a b x real;
solve(a*sin(x)-b*cos(x) == 0,x) % No solution
solve(a*sin(x) == b*cos(x),x) % Again, no solution
solve(a*sin(x)-b*cos(x), x) %Again no solution

All of these (and the variations I've thought of) give no solution. Any thoughts?

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Answer 1

Vineeth Kartha 2016-2-2

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Hi John,

Use the "solve" command as follows:

>> solve(a*sin(x) == b*cos(x),x,'IgnoreProperties',true,'ReturnConditions',true);

This returns a structure expressing the full solution.

Refer to the MATLAB documentation of solve for more information.

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John 2016-2-2

Hmm. Thanks for your answer. I had come across that combination, which for the sake of any other readers gives:

pi*k - (log((a + b*1i)/(a - b*1i))*1i)/2

However I was really hoping to avoid complex exponentials in the the answer (it complicates subsequent manipulation). All my variables are real-valued, and carrying along the full complex form is cumbersome.

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