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)
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.