已知 f(x)=cos²(x+π/3)-1/2 g(x)=1/2sin(2x+2π/3) 求g(x)经怎样变换的f(x)还有h(x)=f(x)-g(x)求h(x)最大值 及相应的x
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![已知 f(x)=cos²(x+π/3)-1/2 g(x)=1/2sin(2x+2π/3) 求g(x)经怎样变换的f(x)还有h(x)=f(x)-g(x)求h(x)最大值 及相应的x](/uploads/image/z/8663514-42-4.jpg?t=%E5%B7%B2%E7%9F%A5+f%28x%29%3Dcos%26sup2%3B%28x%2B%CF%80%2F3%29-1%2F2++g%28x%29%3D1%2F2sin%282x%2B2%CF%80%2F3%29+%E6%B1%82g%EF%BC%88x%EF%BC%89%E7%BB%8F%E6%80%8E%E6%A0%B7%E5%8F%98%E6%8D%A2%E7%9A%84f%EF%BC%88x%EF%BC%89%E8%BF%98%E6%9C%89h%28x%29%3Df%28x%29-g%28x%EF%BC%89%E6%B1%82h%28x%29%E6%9C%80%E5%A4%A7%E5%80%BC+%E5%8F%8A%E7%9B%B8%E5%BA%94%E7%9A%84x)
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已知 f(x)=cos²(x+π/3)-1/2 g(x)=1/2sin(2x+2π/3) 求g(x)经怎样变换的f(x)还有h(x)=f(x)-g(x)求h(x)最大值 及相应的x
已知 f(x)=cos²(x+π/3)-1/2 g(x)=1/2sin(2x+2π/3) 求g(x)经怎样变换的f(x)
还有h(x)=f(x)-g(x)
求h(x)最大值 及相应的x
已知 f(x)=cos²(x+π/3)-1/2 g(x)=1/2sin(2x+2π/3) 求g(x)经怎样变换的f(x)还有h(x)=f(x)-g(x)求h(x)最大值 及相应的x
f(x)=cos²(x+π/3)-1/2 = (1/2)·[2cos²(x+π/3)-1]
= (1/2)·cos(2x+2π/3).二倍角公式
g(x)变换到f(x)可用的方式:
1.g(x)向左平移 Kπ + π/4 个单位
2.g(x)向右平移 Kπ + 3π/4 个单位
h(x) = (1/2)·cos(2x+2π/3) - (1/2)·sin(2x+2π/3)
= [(根2)/2]·cos[(2x+2π/3) + π/4] 《 (根2)/2
所以最大值是:(根2)/2 ,此时 ,cos[(2x+2π/3) + π/4] = 1 ,
有(2x+2π/3) + π/4 = 2kπ ,x = (k - 11/24)π ,k是任意整数