Question

f(x)=sinxcos(π/2-x)-根号3sin(x+π)试求f(x) ,求单调递减区间,由y=sinx怎么平移变换得到f(x )

Answer 1

问：f(x)=sinxcos(π/2-x)-根号3sin(x+π)试求f(x) ,求单调递减区间,由y=sinx怎么平移变换得到f(x )

答：您好，您的问题我已知悉，接下来由我为您解答。最小正周期T=2π/2=π.sin(2x-π/3)=1，即x=kπ+5π/12时，f(x)|max=(2-√3)/2。π/6≤x≤2π/3，则0≤2x-π/3≤π.∴0≤2x-π/3≤π/2，即x∈[π/6，5π/12]时，f(x)单调递增;π/2≤2x-π/3≤π，即x∈[5π/12，2π/3]时，f(x)单调递减。希望对您有所帮助！