Question

手写详细过程谢谢

Answer 1

21、
(1) f(x)=2Asin[(ωx+φ)/2]cos[(ωx+φ)/2]
=Asin(ωx+φ)
设P(p,A)
夹角余弦值为√5/5
p/(√5/2)=√5/5
p=1/2
P(1/2,A)
向量|OP|=√5/2

√[(1/2)^2+A^2]=√5/2
1/4+A^2=5/4
A=1
P(1/2,1)
f(x)=sin(ωx+φ)
sin(ω/2+φ)=1
ω/2+φ=π/2............(1)
向量|OQ|=2
Q(2,0)
sin(2ω+φ)=0
2ω+φ=π................(2)
(2)-(1)：3ω/2=π/2
ω=π/3
代入(2)：2π/3+φ=π
φ=π/3
解析式：f(x)=sin(π/3x+π/3)
(2) h(x)=f(x)*g(x)
=sin(π/3x+π/3)*sin(π/3x)
=1/2{cos[(π/3x+π/3)-π/3x]-cos[(π/3x+π/3)+π/3]}
=1/2[cos(π/3)-cos(π/3x+2π/3)]
=1/2[1/2-cos(π/3x+2π/3)]
=1/4-1/2cos(π/3x+2π/3)
∵-1=<cos(π/3x+2π/3)<=1
∴-1/2=<-1/2cos(π/3x+2π/3)<=1/2
-1/4=<1/4-1/2cos(π/3x+2π/3)<=3/4
h(x)的值域：[-1/4,3/4]