hey guys I am a little confused on where to start! please help?

so find all solutions to this equation by using graphs...

sinx=sin(1/2x)

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- April 30th 2009, 09:32 AMcaseygasparfind all solutions
hey guys I am a little confused on where to start! please help?

so find all solutions to this equation by using graphs...

sinx=sin(1/2x) - April 30th 2009, 10:35 AMMush
- April 30th 2009, 12:07 PMsinewave85
- April 30th 2009, 01:14 PMpflo
In these types of problems, you'll want all of your trig functions to be evaluated at the same number (in this case you've got AND ).

Use the half-angle identity for sine:

So this root equals

Square both sides and you'll have

Then use the pythagorean identity:

You now have

Put this equation into standard form for a quadratic equation and let

You now have

Factor, solve, and put cosine back in for to get: and

Thus, all solutions are and

Don't forget that the range of the arccosine function is limited, so there are three solutions to the original question in every period of the cosine. - April 30th 2009, 01:19 PMpflo
- May 1st 2009, 06:43 AMThe Second Solution