已知函数f(x)=2cos(ωx+π/6),(其中ω>0,x∈R)的最小正周期为10π.(1)求w的值;(2)设a,β∈【0,π/2】,f(5a+5/3π)=-6/5,f(5β-5/6π)=16/17,求cos(a+β)的值.
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![已知函数f(x)=2cos(ωx+π/6),(其中ω>0,x∈R)的最小正周期为10π.(1)求w的值;(2)设a,β∈【0,π/2】,f(5a+5/3π)=-6/5,f(5β-5/6π)=16/17,求cos(a+β)的值.](/uploads/image/z/3711755-11-5.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%EF%BC%88x%EF%BC%89%3D2cos%EF%BC%88%CF%89x%2B%CF%80%2F6%EF%BC%89%2C%EF%BC%88%E5%85%B6%E4%B8%AD%CF%89%EF%BC%9E0%2Cx%E2%88%88R%EF%BC%89%E7%9A%84%E6%9C%80%E5%B0%8F%E6%AD%A3%E5%91%A8%E6%9C%9F%E4%B8%BA10%CF%80.%EF%BC%881%EF%BC%89%E6%B1%82w%E7%9A%84%E5%80%BC%EF%BC%9B%EF%BC%882%EF%BC%89%E8%AE%BEa%2C%CE%B2%E2%88%88%E3%80%900%2C%CF%80%2F2%E3%80%91%2Cf%EF%BC%885a%2B5%2F3%CF%80%EF%BC%89%3D-6%2F5%2Cf%EF%BC%885%CE%B2-5%2F6%CF%80%EF%BC%89%3D16%2F17%2C%E6%B1%82cos%EF%BC%88a%2B%CE%B2%EF%BC%89%E7%9A%84%E5%80%BC.)
已知函数f(x)=2cos(ωx+π/6),(其中ω>0,x∈R)的最小正周期为10π.(1)求w的值;(2)设a,β∈【0,π/2】,f(5a+5/3π)=-6/5,f(5β-5/6π)=16/17,求cos(a+β)的值.
已知函数f(x)=2cos(ωx+π/6),(其中ω>0,x∈R)的最小正周期为10π.
(1)求w的值;
(2)设a,β∈【0,π/2】,f(5a+5/3π)=-6/5,f(5β-5/6π)=16/17,求cos(a+β)的值.
已知函数f(x)=2cos(ωx+π/6),(其中ω>0,x∈R)的最小正周期为10π.(1)求w的值;(2)设a,β∈【0,π/2】,f(5a+5/3π)=-6/5,f(5β-5/6π)=16/17,求cos(a+β)的值.
w(x+10pi) - wx = 2pi
10w = 2
w = 1/5
f(5A+5/3 pi) = 2*cos(A+pi/3+pi/6) = -2sinA = -6/5,sin A= 3/5,cos A = 4/5
f(5B-5/6 pi) = 2 cos(B - pi/6 + pi/6) = 2cosB = 16/17,cosB= 8/17,sinA = 15/17
cos(A+B) = cosAcosB-sinAsinB = 4/5*8/17 - 3/5*15/17 = -13/85
T=10π=2π/ω ω=1/5 f(x)=2cos[(1/5)x+π/6] 全部展开 T=10π=2π/ω ω=1/5 f(x)=2cos[(1/5)x+π/6] 收起
f﹙5α+5π/3﹚=2cos(α+π/3+π/6)=-6/5
即 -2sinα=-6/5
即 sinα=3/5,则 cosα=4/5
f(5β-5π/6)=2cos(β-π/6+π/6)=16/17
f﹙5α+5π/3﹚=2cos(α+π/3+π/6)=-6/5
即 -2sinα=-6/5
即 sinα=3/5,则 cosα=4/5
f(5β-5π/6)=2cos(β-π/6+π/6)=16/17
即 cosβ=8/17,则sinβ=15/17
cos(α+β)
=cosαcosβ-sinαsinβ
=(4/5)*(8/17)-(3/5)(15/17)
=-13/85