已知向量a=(cos(3x/4),sin(3x/4)),向量b=(cos(x/4+π/3),-sin(x/4+π/3))1:令f(x)=(向量a+向量b)的平方,求f(x)的解析式和单调区间2:若x属于-π/6,5π/6都是闭区间,求f(x)的最大最小
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![已知向量a=(cos(3x/4),sin(3x/4)),向量b=(cos(x/4+π/3),-sin(x/4+π/3))1:令f(x)=(向量a+向量b)的平方,求f(x)的解析式和单调区间2:若x属于-π/6,5π/6都是闭区间,求f(x)的最大最小](/uploads/image/z/2667460-4-0.jpg?t=%E5%B7%B2%E7%9F%A5%E5%90%91%E9%87%8Fa%3D%EF%BC%88cos%EF%BC%883x%2F4%EF%BC%89%2Csin%EF%BC%883x%2F4%EF%BC%89%EF%BC%89%2C%E5%90%91%E9%87%8Fb%3D%EF%BC%88cos%EF%BC%88x%2F4%2B%CF%80%2F3%EF%BC%89%2C-sin%EF%BC%88x%2F4%2B%CF%80%2F3%EF%BC%89%EF%BC%891%EF%BC%9A%E4%BB%A4f%EF%BC%88x%EF%BC%89%3D%EF%BC%88%E5%90%91%E9%87%8Fa%2B%E5%90%91%E9%87%8Fb%EF%BC%89%E7%9A%84%E5%B9%B3%E6%96%B9%2C%E6%B1%82f%EF%BC%88x%EF%BC%89%E7%9A%84%E8%A7%A3%E6%9E%90%E5%BC%8F%E5%92%8C%E5%8D%95%E8%B0%83%E5%8C%BA%E9%97%B42%EF%BC%9A%E8%8B%A5x%E5%B1%9E%E4%BA%8E-%CF%80%2F6%2C5%CF%80%2F6%E9%83%BD%E6%98%AF%E9%97%AD%E5%8C%BA%E9%97%B4%2C%E6%B1%82f%EF%BC%88x%EF%BC%89%E7%9A%84%E6%9C%80%E5%A4%A7%E6%9C%80%E5%B0%8F)
已知向量a=(cos(3x/4),sin(3x/4)),向量b=(cos(x/4+π/3),-sin(x/4+π/3))1:令f(x)=(向量a+向量b)的平方,求f(x)的解析式和单调区间2:若x属于-π/6,5π/6都是闭区间,求f(x)的最大最小
已知向量a=(cos(3x/4),sin(3x/4)),向量b=(cos(x/4+π/3),-sin(x/4+π/3))
1:令f(x)=(向量a+向量b)的平方,求f(x)的解析式和单调区间
2:若x属于-π/6,5π/6都是闭区间,求f(x)的最大最小值
已知向量a=(cos(3x/4),sin(3x/4)),向量b=(cos(x/4+π/3),-sin(x/4+π/3))1:令f(x)=(向量a+向量b)的平方,求f(x)的解析式和单调区间2:若x属于-π/6,5π/6都是闭区间,求f(x)的最大最小
1.f(x)=[cos(3x/4)+cos(x/4+π/3)]^2+[sin(3x/4)-sin(x/4+π/3)]^2
=cos^2(3x/4)+sin^2(3x/4)+cos^2(x/4+π/3)+sin^2(x/4+π/3)
+2cos(3x/4)cos(x/4+π/3)-2sin(3x/4)sin(x/4+π/3)
=1+1+2cos(3x/4+x/4+π/3)=2cos(x+π/3)+2
单增区间(2kπ-π/3,2kπ+2π/3),单减区间(2kπ+2π/3,2kπ+5π/3),极值点2kπ-π/3,2kπ+2π/3,k∈Z
2.[-π/6,5π/6]包含一个极小值点2π/3,两个端点中f(-π/6)较大.所以最大值是f(-π/6)=根3+2,
最小值是f(2π/3)=0