求函数y=sin(x+20)-cos(x-10)的值域y=sin(x+20)-cos(x-10)的值域 我这么做对吗？y=sin(x-10+30) - cos(x-10)y=sin(x-10)cos30 + sin30(x-10) - cos (x-10)y=sin(x-10)cos30 - sin30(x-10)y=sin(x-10-30)y=sin(x-40)所以值域为 -1，1
问题描述：
求函数y=sin(x+20)-cos(x-10)的值域
y=sin(x+20)-cos(x-10)的值域 我这么做对吗？
y=sin(x-10+30) - cos(x-10)
y=sin(x-10)cos30 + sin30(x-10) - cos (x-10)
y=sin(x-10)cos30 - sin30(x-10)
y=sin(x-10-30)
y=sin(x-40)
所以值域为 -1，1
答
[-根号2/2,根号2/2]
答
y=sin(x+20)-cos(x-10)
x-10=t
y=sin(t+30)-cost=(√3/2)sint-(1/2)cost=-cos(t+60)
值域[-1,1]
答
y=sin(x+20)-cos(x-10)
=sin(x+20)-sin[90-(x-10)]
=sin(x+20)-sin(100-x)
=sin(x+20)-sin[180-(100-x)]
=sin(x+20)-sin(x+80)
和差化积
=2cos(x+50)*sin(-30)
=-cos(x+50)
所以值域[-1,1]