For asin(x) + bcos(x): range is [-sqrt(a^{2+b}^2), sqrt(a^{2+b}^2)]. For a*$sin^2$(x) + b*sin(x)cos(x) + c$cos^2$(x): rewrite using double angle formulas to get a linear combination of sin2x and cos2x plus a constant, then apply auxiliary angle method.