已知函数y=sin'x+2√3sinxcosx-cos'x

3个回答

  • (1)y=sin'x+2√3sinxcosx-cos'x

    =√3*2sinxcosx-(cos'x-sin'x)

    =√3sin2x-cos2x

    =2(√3/2sin2x-1/2cos2x)

    =2(cosπ/6sin2x-sinπ/6cos2x)

    =2sin(2x-π/6)

    ∴T=2π/2=π

    ∴ymin=-2

    (2)-π/2+2kπ≤2x-π/6≤π/2+2kπ

    -π/6+2kπ≤2x≤2π/3+2kπ

    -π/12+kπ≤x≤π/4+kπ

    又0≤x≤π

    所以增区间为x∈[0,π/4]∪[11/12π,π]