数学已知函数f(x)=sin(x+θ)+cos(x+θ)的定义域为R.(1)当θ=π/2时,求f(x)的单调递增区间.
RT
杜世臣回答:
f(x)=sin(x+θ)+cos(x+θ)
=√2[√2/2sin(x+θ)+√2/2cos(x+θ)]
=√2[sin(x+θ)cosπ/4+cos(x+θ)sinπ/4]
=√2sin(x+θ+π/4)
当θ=π/2时,f(x)=√2sin(x+θ+π/4)
=√2sin(x+3π/4)
当x+3π/4∈[2kπ-π/2,2kπ+π/2]时,f(x)单调递增;
此时x∈[2kπ-5π/4,2kπ-π/4]其中k∈Z.
相关文章: