Question

已知函数f(x)=Asin(wx+φ) (A>0,w>0,│φ│

Answer 1

(1) A=1
T/2=π/3-(-π/6)=π/2
T=π
ω=2π/T=2
f(x)=sin(2x+φ)过(-π/6,0)
sin(-π/6+φ)=0
-π/6+φ=0
φ=π/6
f(x)=sin(2x+π/6)
(2)
∵tanα=3>0
∴α为第一、三象限角,为计算方便,假设为第一象限角
sinα/cosα=3
sinα=3cosα
sin^2α=9cos^2α
1=10cos^2α
cosα=1/√10
sinα=3/√10
g(x)=√3f(x-π/4)+f(x)
=√3sin[2(x-π/4)+π/6]+sin(2x+π/6)
=√3sin(2x+π/6-π/2)+sin(2x+π/6)
=-√3cos(2x+π/6)+sin(2x+π/6)
=2sin(2x+π/6-π/3)
=2sin(2x-π/6)
=2sin2xcosπ/6-2cos2xsinπ/6
=2√3sinxcosx-2cos^2x+1
g(α)=2√3sinαcosα-2cos^2α+1
=2√3*3/√10*1/√10-2(1/√10)^2+1
=3√3/5-1/5+1
=(4+3√3)/5