(1)求y=根号3sinx+cosx的周期,最大值递增区间(2)若cosa+2sina=-根号5,求tana的值
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![(1)求y=根号3sinx+cosx的周期,最大值递增区间(2)若cosa+2sina=-根号5,求tana的值](/uploads/image/z/11416111-7-1.jpg?t=%EF%BC%881%EF%BC%89%E6%B1%82y%3D%E6%A0%B9%E5%8F%B73sinx%2Bcosx%E7%9A%84%E5%91%A8%E6%9C%9F%2C%E6%9C%80%E5%A4%A7%E5%80%BC%E9%80%92%E5%A2%9E%E5%8C%BA%E9%97%B4%EF%BC%882%EF%BC%89%E8%8B%A5cosa%2B2sina%3D-%E6%A0%B9%E5%8F%B75%2C%E6%B1%82tana%E7%9A%84%E5%80%BC)
(1)求y=根号3sinx+cosx的周期,最大值递增区间(2)若cosa+2sina=-根号5,求tana的值
(1)求y=根号3sinx+cosx的周期,最大值
递增区间(2)若cosa+2sina=-根号5,求tana的值
(1)求y=根号3sinx+cosx的周期,最大值递增区间(2)若cosa+2sina=-根号5,求tana的值
(1) y=√3sinx+cosx
=2(√3/2sinx+1/2cosx)
=2(sinxcosπ/6+sinπ/6cosx)
=2sin(x+π/6)
周期T=2π
最大值=2
递增区间:2kπ-π/2≤x+π/6
(1)y=√3sinx+cosx
=2sin(x+π/3)
∴T=2π/1=2π,ymax=2
-π/2+2kπ≤ x+π/3≤π/2+2kπ,k∈Z
-5π/6+2kπ≤x≤π/6+2kπ,k∈Z
单调递增区间为:[-5π/6+2kπ,π/6+2kπ],k∈z
(2)cosa+2sina=√5
两边平方:cos&...
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(1)y=√3sinx+cosx
=2sin(x+π/3)
∴T=2π/1=2π,ymax=2
-π/2+2kπ≤ x+π/3≤π/2+2kπ,k∈Z
-5π/6+2kπ≤x≤π/6+2kπ,k∈Z
单调递增区间为:[-5π/6+2kπ,π/6+2kπ],k∈z
(2)cosa+2sina=√5
两边平方:cos²a+4sin²a+4cosasina=5
两边同除以(sin²a+cos²a),得:
tan²a-4tana+4=0
(tana-2)²=0
tana=2
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