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

1. ## 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?

2. ## Re: How to solve, for example, sin x = sin (2.4x)

Originally Posted by Mikael
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