作业帮已知向量a=(sinx,3/2),b=(cosx,-1),求f(x)=(a+b)b在[-π/2,0]上的值域
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![已知向量a=(sinx,3/2),b=(cosx,-1),求f(x)=(a+b)b在[-π/2,0]上的值域](/uploads/image/z/5293827-27-7.jpg?t=%E5%B7%B2%E7%9F%A5%E5%90%91%E9%87%8Fa%3D%28sinx%2C3%2F2%29%2Cb%3D%28cosx%2C-1%29%2C%E6%B1%82f%28x%29%3D%28a%2Bb%29b%E5%9C%A8%5B-%CF%80%2F2%2C0%5D%E4%B8%8A%E7%9A%84%E5%80%BC%E5%9F%9F)
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已知向量a=(sinx,3/2),b=(cosx,-1),求f(x)=(a+b)b在[-π/2,0]上的值域
已知向量a=(sinx,3/2),b=(cosx,-1),求f(x)=(a+b)b在[-π/2,0]上的值域
已知向量a=(sinx,3/2),b=(cosx,-1),求f(x)=(a+b)b在[-π/2,0]上的值域
a+b=(sinx+cosx,1/2)
(a+b)b=sinxcosx+cos^2x-1/2
=(1/2)(sin2x+cos2x)
=(2^(1/2))/2)(sin(2x+π/4)
x∈[-π/2,0] 所以 2x+π/4∈[0,π/4]
所以函数的值域为 [0,1/2]