急!数学小题!已知f(x)=根号3*sin2x-2sin^2x.若x属于[-π/6,π/3],求f(x)的值域
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急!数学小题!
已知f(x)=根号3*sin2x-2sin^2x.若x属于[-π/6,π/3],求f(x)的值域
已知f(x)=根号3*sin2x-2sin^2x.若x属于[-π/6,π/3],求f(x)的值域
![急!数学小题!已知f(x)=根号3*sin2x-2sin^2x.若x属于[-π/6,π/3],求f(x)的值域](/uploads/image/z/16510176-0-6.jpg?t=%E6%80%A5%21%E6%95%B0%E5%AD%A6%E5%B0%8F%E9%A2%98%21%E5%B7%B2%E7%9F%A5f%28x%29%3D%E6%A0%B9%E5%8F%B73%2Asin2x-2sin%5E2x.%E8%8B%A5x%E5%B1%9E%E4%BA%8E%5B-%CF%80%2F6%2C%CF%80%2F3%5D%2C%E6%B1%82f%28x%29%E7%9A%84%E5%80%BC%E5%9F%9F)
f(x)=根号3*sin2x-2sin^2x=√3sin2x+1-cos2x=1+2(cosπ/6sin2x-sinπ/6cos2x)
=1+2sin(2x-π/6)
x属于[-π/6,π/3]时,2x-π/6属于[-π/2,π/2],该区间内单增
f(-π/6)=1-2=-1
f(π/3)=1+2=3
值域[-1,3]
=1+2sin(2x-π/6)
x属于[-π/6,π/3]时,2x-π/6属于[-π/2,π/2],该区间内单增
f(-π/6)=1-2=-1
f(π/3)=1+2=3
值域[-1,3]
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