已知函数f(x)=sin平方+sinxcosx1,求tana的值及对称轴方程2,求f(x)在x属于[0,兀]的单调递增区间
问题描述:
已知函数f(x)=sin平方+sinxcosx
1,求tana的值及对称轴方程
2,求f(x)在x属于[0,兀]的单调递增区间
答
f(x)=(sinx)平方+sinxcosx
= 1/2(1-cos2x) + 1/2sin2x
= 1/2 - 1/2cos2x +1/2sin2x
= 1/2 + √2/2(sin2xcosπ/4-cos2xsinπ/4)
= 1/2 + √2/2 sin(2x-π/4)
x∈[0,π]
2x∈[0,2π]
2x-π/4∈[-π/4,7π/4]
当2x-π/4∈[-π/4,π/2)和∈[3π/2,7π/4)时单调增
所以单调增区间:[0,3π/8)和∈[7π/8,π)