Posted by Megan on Wednesday, December 8, 2010 at 8:20pm.
Use the identity sin²(x)=1-cos²(x).
So
2sin^2x+3cosx=3 becomes
2cos²(x)-3cos(x)-1=0
Solve the quadratic for cos(x),
I get cos(x)=1 or cos(x)=1/2
On the interval [0,2π], each value of cos(x) has two solutions for a total of 4 values of x.
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