三角函数
⑴2sina-cosa=√3 sina,则sina等于多少? ⑵ 已知函数得最大值是3,并且在区间[-π/4+3kπ/4,π/8+3kπ/4]k∈Z是增函数,在[π/8+3kπ/4,π/2+3kπ/4]k∈Z上是减函数,求f=(x)
(1) (2+√3)sina=cosa,两边平方,得(7+√3)sin²a=1-cos²a, ∴ 4sin²a=(2-√3), 16sin²a=2(√3-1)², ∴ sina=±(√6-√2)/4. (2) 由已知条件知y=f(x)=3sin(ωx+φ)在x=π/8+3kπ/4时,y=3 -π/2+2kπ≤ωx+φ≤π/2+2kπ时y是增函数,即[(-π/2)-φ]/ω+(2kπ-φ)/ω≤x≤[(π/2)-φ]/ω+(2kπ-φ)/ω, ∴ [(-π/2)-φ]/ω=(π/4),[(π/2)-φ]/ω=π/8,解得φ=π/6, 半周期T/2=[(π/8)+(3kπ/4)]-[(-π/4)+(3kπ/4)]=3π/8, ∴ T=3π/4=2π/ω, ∴ ω=8/3 ∴ f(x)=3sin[(8x/3)+(π/6)]
答:(2sina-sin2a)/(2sina+sin2a) = (2sina-2sinacosa)/(2sina+2sinacosa) = (1-cosa)/(1+...详情>>
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