f(x)=2x^2+3x-2

f(sinx)=2sin^2(x)+3sin(x)-2

2sin^2(x)+3sin(x)-2=2(1-cos^2(x))+3sin(x)-2=2-2cos^2(x)+3sin(x)-2=3sin(x)-2cos^2(x)

f(sinx)=3sin(x)-2cos^2(x)