已知函数f(x)=2根号3sinxcosx+cos2x 求f(π/6)的值
问题描述:
已知函数f(x)=2根号3sinxcosx+cos2x 求f(π/6)的值
答
f(x)=2√3sinxcosx+cos2x
=√3sin2x+cos2x
=2(√3/2sin2x+1/2cos2x)
=2sin(2x+π/6)
f(π/6)=2sin(2*π/6+π/6)
=2sin(3*π/6)
=2sinπ/2
=2��X�ʣ�0����/4��������f(x)��ֵ������ллX∈(0,π/4)2x∈(0,π/2)2x+π/6∈(π/6,π/2+π/6)1/2