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Math Help - How to solve, for example, sin x = sin (2.4x)

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    How to solve, for example, sin x = sin (2.4x)

    Hi!

    I had a simple problem to solve, sin x = sin 2x, and did it by using the identity sin (2x) = 2 sin (x) cos(x), but what then struck me is that I'm completely clueless how I'd even start solving a problem like sin x = sin (2.4x), or where there essentially are decimals involved and not simple integers.
    Are there identities available for these non-integer problems or is the approach completely different?
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    Re: How to solve, for example, sin x = sin (2.4x)

    Quote Originally Posted by Mikael View Post
    Hi!

    I had a simple problem to solve, sin x = sin 2x, and did it by using the identity sin (2x) = 2 sin (x) cos(x), but what then struck me is that I'm completely clueless how I'd even start solving a problem like sin x = sin (2.4x), or where there essentially are decimals involved and not simple integers.
    Are there identities available for these non-integer problems or is the approach completely different?
    There are no such identities. You are basically stuck with three options: First you can change the 2.4 to another decimal using the sine/cosine addition formulas, the half angle formulas, etc. Second you can do it numerically. Third: You can operate both sides with the inverse sine function: sin^{-1}(sin(x)) = sin^{-1}(sin(2.4x)) but you need to be very careful about the domains. It's very easy to find spurious solutions or miss some entirely.

    -Dan
    Thanks from Mikael
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