Question

一道高中简单三角函数题.已知函数f(x)=2asinxcosx+2bcos²x,且f(0)=8,f(π/6)=

Answer 1

题目呢

f(x)=2asinxcosx+2bcos²x,且f(0)=8,f(π/6)=12

求得b=4

2sinxcosx=sin2x

2cos²x=cos2x +1

f(x)=asin2x+b（cos2x +1）

f(0)=2b=8

b=4

f(π/6)=a√3/2 + b3/2=a√3/2 +6=12

a√3/2 =6

a=4√3