若3sin^2θ+√3sinθcosθ+4cos^2θ+k化成sin（θ+b）（0《b《Π）的形式,求k和b辅助角公式

Question

若3sin^2θ+√3sinθcosθ+4cos^2θ+k化成sin（θ+b）（0《b《Π）的形式,求k和b
辅助角公式

Answer 1

3sin^2θ+√3sinθcosθ+4cos^2θ+k
=3sin^2θ+4cos^2θ+√3sinθcosθ+k
=3sin^2θ+3cos^2θ+cos^2θ+√3sinθcosθ+k
=3+cos^2θ+√3sinθcosθ+k
=cos^2θ+√3sinθcosθ+k+3
=(1+cos2θ)/2+√3/2*sin2θ+k+3
=1/2*cos2θ+√3/2*sin2θ+k+3+1/2
=sinπ/6*cos2θ+cosπ/6sin2θ+k+7/2
=sin(π/6+2θ)+k+7/2
b=π/6,k+7/2=0
b=π/6
k=-7/2