已知函数f(x)=sinxcosΦ+cosxsinΦ(其中x∈R，0<Φ<π)，且函数y=f(2x+π/4)的图像关于x=π/6对称

显示全部楼层 · 2013-2-17 00:14:05

f(x)=sinxcosΦ+cosxsinΦ=sin(x+Φ)(其中x∈R，0<Φ<π)，f(2x+π/4)=sin(2x+π/4+Φ)函数y=f(2x+π/4)的图像关于x=π/6对称2*π/6+π/4+Φ=kπ+π/2（k∈Z）得Φ=kπ-π/12（k∈Z）由0<Φ<π得k=1，Φ=11π/12∴f(x)=sin(x+11π/12)若f(a-2π/3）=根号2/4，有sin(a-2π/3+11π/12)=sin(a+π/4）=根号2/2*（sina+cosa）=根号2/4∴sina+cosa=1/2两侧平方得sin2a+2sinacosa+cos2a=1/4∴sin...

千问 · 2013-2-17 00:14:05

f(x)=sinxcosΦ+cosxsinΦ=sin(x+Φ)函数y=f(2x+π/4)=sin(2x+π/4+Φ)图像关于x=π/6对称∴x=π/6时，2×π/6+π/4+Φ=kπ+π/2,k∈Z∴Φ=kπ-π/12,k∈Z∵0<Φ<π∴当k=1时，Φ=11π/12∴f(x)=sin(x+11π/12)∵f(a-2π/3）=...