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(_数学解答

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

人气：204 ℃　时间：2020-03-29 19:02:02

解答

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]