已知函數(shù)y=Asin(Wx+φ)(A>0,w>0,-π/2

數(shù)學(xué)人氣：551 ℃時(shí)間：2020-06-19 19:59:54

優(yōu)質(zhì)解答

1.同一個(gè)周期內(nèi),當(dāng)x=π/4時(shí),y取最大值2,當(dāng)X=7π/12,y取最大值為-2
A=2
7π/12-π/4=π/3=T/2 (T為周期) T=2π/3
T=2π/w=2π/3 w=3
f(x)=2sin(3x+φ) 過(guò)（π/4,2）
sin(3π/4+φ)=1 3π/4+φ=π/2 φ=-π/4
(1) f(x)=2sin(3x-π/4)
(2) 2sin(3x-π/4)=√3
sin(3x-π/4)=√3/2
3x-π/4=2kπ+π/3或3x-π/4=2kπ+2π/3
x=2kπ/3+7π/36或x=2kπ/3+11π/36
x∈[0,2π]
所以x=7π/36,11π/36,31π/36,55π/36,35π/36,59π/36
(3) 有6個(gè)根
x1+x2=π/2
6個(gè)根之和=3π/2