三角函数最大值和最小值,
问题描述:
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)
答
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