三角函数最大值和最小值,
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三角函数最大值和最小值,
Find the maximum and minimum values of the function.(Round your answer to two decimal places.)y=(cos x )/(5+sin x)
Find the maximum and minimum values of the function.(Round your answer to two decimal places.)y=(cos x )/(5+sin x)
![三角函数最大值和最小值,](/uploads/image/z/15110912-56-2.jpg?t=%E4%B8%89%E8%A7%92%E5%87%BD%E6%95%B0%E6%9C%80%E5%A4%A7%E5%80%BC%E5%92%8C%E6%9C%80%E5%B0%8F%E5%80%BC%2C)
y=cosx/(5+sinx)
y'=[-sinx(5+sinx)-cosx cosx]/(5+sinx)^2=-(5sinx+1)/(5+sinx)^2=0
---> sinx=-1/5
所以有:
最大值当sinx=-1/5,cosx=2√6/5,ymax=2√6/(25-1)=√6/12=0.20
最小值当sinx=-1/5,cosx=-2√6/5,ymax=-2√6/(25-1)=-√6/12 =-0.20
y'=[-sinx(5+sinx)-cosx cosx]/(5+sinx)^2=-(5sinx+1)/(5+sinx)^2=0
---> sinx=-1/5
所以有:
最大值当sinx=-1/5,cosx=2√6/5,ymax=2√6/(25-1)=√6/12=0.20
最小值当sinx=-1/5,cosx=-2√6/5,ymax=-2√6/(25-1)=-√6/12 =-0.20