已知函数fx=2sin(2x+Φ)对任意实数x恒有f(π/3-x)=f(π/3+x)

显示全部楼层 · 2012-12-24 21:12:47

(1)缺少g(x)的表达式应该是g(x)=2cos(2x+Φ)∵f(π/3+x)=f(π/3-x)∴2sin(2π/3+2x+Φ)=2sin(2π/3-2x+Φ)∴2π/3+Φ=nπ/2(n=1、3、5、7、9、……)g(π/3)=2cos(2π/3+Φ)=2cos(nπ/2)∵cos(π/2)=0；cos(3π/2)=0；cos(5π/2)=0；cos(7π/2)=0……∴g(π/3)=0如果题目是求f(π/3) x=π/3是对称轴，则f(π/3)=2或-2(2)2π/3+Φ=nπ/2(n=1、3、5、7、9、……)当n=3时，2π/3+Φ=3π/2Φ取最小正值，为3π/2-2π/3=5π/6 ...

千问 · 2012-12-24 21:12:47

第一问是求f(π/3) 吧…：x=π/3是对称轴，则f(π/3)=2或-2第二问：2*π/3+Φ=π/2+kπ (k为整数)，得k=1时Φ取得最小正值，Φ=5π/6...

千问 · 2012-12-24 21:12:47

应该是g(x)=2cos(2x+Φ)∵f(π/3+x)=f(π/3-x)∴2sin(2π/3+2x+Φ)=2sin(2π/3-2x+Φ)∴2π/3+Φ=nπ/2(n=1、3、5、7、9、……)g(π/3)=2cos(2π/3+Φ)=2cos(nπ/2)∵cos(π/2)=0；cos(3π/2)=0；cos(5π/2)=0；cos(7π/2...