已知函数g(x)=1/2sin(2x+2π/3)的图像向左平移π/4个单位长度,再向上平移1/2个单位长度,得到f(x)=acos^2(x+π/3)的图像(1) 求实数a,b的值(2)设函数φ(x)=g(x)-根号3f(x) 求φ(x)的单调增区间漏了东西 重
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![已知函数g(x)=1/2sin(2x+2π/3)的图像向左平移π/4个单位长度,再向上平移1/2个单位长度,得到f(x)=acos^2(x+π/3)的图像(1) 求实数a,b的值(2)设函数φ(x)=g(x)-根号3f(x) 求φ(x)的单调增区间漏了东西 重](/uploads/image/z/1985187-3-7.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0g%28x%29%3D1%2F2sin%282x%2B2%CF%80%2F3%29%E7%9A%84%E5%9B%BE%E5%83%8F%E5%90%91%E5%B7%A6%E5%B9%B3%E7%A7%BB%CF%80%2F4%E4%B8%AA%E5%8D%95%E4%BD%8D%E9%95%BF%E5%BA%A6%2C%E5%86%8D%E5%90%91%E4%B8%8A%E5%B9%B3%E7%A7%BB1%2F2%E4%B8%AA%E5%8D%95%E4%BD%8D%E9%95%BF%E5%BA%A6%2C%E5%BE%97%E5%88%B0f%28x%29%3Dacos%5E2%28x%2B%CF%80%2F3%29%E7%9A%84%E5%9B%BE%E5%83%8F%EF%BC%881%EF%BC%89+%E6%B1%82%E5%AE%9E%E6%95%B0a%2Cb%E7%9A%84%E5%80%BC%EF%BC%882%EF%BC%89%E8%AE%BE%E5%87%BD%E6%95%B0%CF%86%28x%29%3Dg%28x%29-%E6%A0%B9%E5%8F%B73f%28x%29+%E6%B1%82%CF%86%28x%29%E7%9A%84%E5%8D%95%E8%B0%83%E5%A2%9E%E5%8C%BA%E9%97%B4%E6%BC%8F%E4%BA%86%E4%B8%9C%E8%A5%BF+%E9%87%8D)
已知函数g(x)=1/2sin(2x+2π/3)的图像向左平移π/4个单位长度,再向上平移1/2个单位长度,得到f(x)=acos^2(x+π/3)的图像(1) 求实数a,b的值(2)设函数φ(x)=g(x)-根号3f(x) 求φ(x)的单调增区间漏了东西 重
已知函数g(x)=1/2sin(2x+2π/3)的图像向左平移π/4个单位长度,再向上平移1/2个单位长度,得到f(x)=acos^2(x+π/3)的图像
(1) 求实数a,b的值
(2)设函数φ(x)=g(x)-根号3f(x) 求φ(x)的单调增区间
漏了东西 重发一遍
已知函数g(x)=1/2sin(2x+2π/3)的图像向左平移π/4个单位长度,再向上平移1/2个单位长度,得到f(x)=acos^2(x+π/3)+b的图像
(1) 求实数a,b的值
(2)设函数φ(x)=g(x)-根号3f(x) 求φ(x)的单调增区间
已知函数g(x)=1/2sin(2x+2π/3)的图像向左平移π/4个单位长度,再向上平移1/2个单位长度,得到f(x)=acos^2(x+π/3)的图像(1) 求实数a,b的值(2)设函数φ(x)=g(x)-根号3f(x) 求φ(x)的单调增区间漏了东西 重
(1)g(x)=1/2sin(2x+2π/3)=g(x)=1/2sin[2(x+π/3)]
向左平移π/4个单位长度,再向上平移1/2个单位长度后
f(x)=1/2sin[2(x+π/3+π/4)]+1/2
=1/2sin[2(x+π/3)+π/2]+1/2
=1/2cos[2(x+π/3)]+1/2
=1/2[2cos^2(x+π/3)-1]+1/2
=cos^2(x+π/3)
∴ a=1 b=0
(2)φ(x)=g(x)-√3f(x)
=1/2sin[2(x+π/3)]-√3cos^2(x+π/3)
=1/2sin[2(x+π/3)]-√3[1/2cos[2(x+π/3)]+1/2]
=1/2sin[2(x+π/3)]-√3/2cos[2(x+π/3)]-√3/2
=sin[2(x+π/3)-π/6]-√3/2
=sin[2x+π/2]-√3/2
=cos2x-√3/2
所以 φ(x)的单调增区间由下式确定
-π+2kπ≤2x≤2kπ
即 -π/2+kπ≤x≤kπ (k=0,±1,±2,…)为所求的增区间