函数y=sin(x+10°)+cos(x+40°),(x∈R)的最大值是______.-数学

题目简介

函数y=sin(x+10°)+cos(x+40°),(x∈R)的最大值是______.-数学

题目详情

函数y=sin(x+10°)+cos(x+40°),(x∈R)的最大值是______.
题型:填空题难度:中档来源:宁波模拟

答案

函数y=sin(x+10°)+cos(x+40°)
=sin(x+10°)+cos(x+10°+30°)
=sin(x+10°)+cos(x+10°)cos30°-sin(x+10°)sin30°
=class="stub"1
2
sin(x+10°)+
3
2
cos(x+10°)
=sin(x+70°)
∵y=sin(x+70°)的最大值是1
∴函数y=sin(x+10°)+cos(x+40°)(x∈R)的最大值是1
故答案为:1

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