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若f(x)=asin^3x+b(³√x)cos³x+4(a,bεR),且f(sin10°)=5,则f

来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/05/25 05:23:21
若f(x)=asin^3x+b(³√x)cos³x+4(a,bεR),且f(sin10°)=5,则f(cos100°)=____
f(x)=a(sinx)^3+b(³√x)cos³x+4
cos100°=cos(90°+10°)=-sin(10°)
f(-x)= -a(sinx)^3 -b(³√x)cos³x + 4
f(sin10°)=5
a(sin(sin10°))^3+b(³√(sin10°))cos³(sin10°)+4=5
a(sin(sin10°))^3+b(³√(sin10°))cos³(sin10°)=1
-a(sin(sin10°))^3-b(³√(sin10°))cos³(sin10°)= -1
-a(sin(sin10°))^3-b(³√(sin10°))cos³(sin10°)+4=3
f(cos100°)=f(-sin10°)=3