1.已知cos(x+π/4)=3/5,π/2

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/18 04:02:58

1.已知cos(x+π/4)=3/5,π/2
1.已知cos(x+π/4)=3/5,π/2

1.已知cos(x+π/4)=3/5,π/2
(1)因为cos(x+π/4)=3/5,且π/2所以3π/4则5π/4又因为cos(x+π/4)=√2/2(cosx-sinx)=3/5,且sin^2x+cos^2x=1
得sinx=-7√2/10,cosx=-√2/10
且cos(2x+π/4)=√2/2(cos^2x-sin^2x-2sinxcosx)=-31√2/50
(2)由已知可得y=(sin^2x+cos^2x)(sin^2x-cos^2x)+√3sin2x
可得y=-2(√3/2sin2x-1/2cos2x)=-2sin(2x-π/6)
则可看出最小正周期为π,最小值为-2
〔0,π〕的单调增区间为(0,π/3)并(5π/6,7π/12)