已知cos(a+π/3)=-3/5且π/6

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已知cos(a+π/3)=-3/5且π/6

已知cos(a+π/3)=-3/5且π/6
已知cos(a+π/3)=-3/5且π/6

已知cos(a+π/3)=-3/5且π/6
cos(a+π/3)=-3/5
cosacosπ/3-sinasinπ/3 = -3/5
1/2 cosa - √3/2 sina = -3/5
5cosa - 5√3sina = -6
5cosa + 6 = 5√3sina
(5cosa + 6)^2 = (5√3sina)^2
25cos^2a+60cosa+36 = 75sin^2a
25cos^2a+60cosa+36 = 75(1-cos^2a)
100cos^2a+60cosa=39
(10cosa+3)^2=48
10cosa+3=±4√3
cosa = (-3-4√3)/10,或cosa = (-3+4√3)/10
π/6

π/6sina>1/2。-1/2cos(a+π/3)=-3/5,即cosacosπ/3-sinasinπ/3=-3/5,即1/2cosa-√3sina=-3/5
因为cos²a+sin²a=1,则带入求解,在对照上面的cosa的取值进行取舍