设函数f(x)=3sin(ωx+π/6),ω>0,x∈(-∞,+∞),且以π/2为最小正周期.⑴求f(0);⑵求f(x)的解析式;⑶已知f(α/4+π/12)=9/5,求sinα的值.

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设函数f(x)=3sin(ωx+π/6),ω>0,x∈(-∞,+∞),且以π/2为最小正周期.⑴求f(0);⑵求f(x)的解析式;⑶已知f(α/4+π/12)=9/5,求sinα的值.

设函数f(x)=3sin(ωx+π/6),ω>0,x∈(-∞,+∞),且以π/2为最小正周期.⑴求f(0);⑵求f(x)的解析式;⑶已知f(α/4+π/12)=9/5,求sinα的值.
设函数f(x)=3sin(ωx+π/6),ω>0,x∈(-∞,+∞),且以π/2为最小正周期.
⑴求f(0);⑵求f(x)的解析式;⑶已知f(α/4+π/12)=9/5,求sinα的值.

设函数f(x)=3sin(ωx+π/6),ω>0,x∈(-∞,+∞),且以π/2为最小正周期.⑴求f(0);⑵求f(x)的解析式;⑶已知f(α/4+π/12)=9/5,求sinα的值.
(1)f(0)=3sin(ω*0+π/6)
=3sin(π/6)
=3/2
(2)∵π/2为f(x)最小正周期,ω>0
∴ω=2π/(π/2)
=4
∴f(x)=3sin(4x+π/6)
(3)f(α/4+π/12)=3sin[4(α/4+π/12)+π/6]
=3sin(α+π/2)
=3cosα
∵f(α/4+π/12)=9/5
∴3cosα=9/5
∴cosα=3/5
∵sin^2 α+cos^2 α=1
∴sinα=±4/5