Question

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

Answer 1

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