一道高中三角函数的数学题,sin(α+π/3)=1/4α∈(π/6,π)求sin(α)的值.我解到sin(α+π/3)=1/2sinα+(根号3)/2cos=1/4请讲清楚
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![一道高中三角函数的数学题,sin(α+π/3)=1/4α∈(π/6,π)求sin(α)的值.我解到sin(α+π/3)=1/2sinα+(根号3)/2cos=1/4请讲清楚](/uploads/image/z/3833614-46-4.jpg?t=%E4%B8%80%E9%81%93%E9%AB%98%E4%B8%AD%E4%B8%89%E8%A7%92%E5%87%BD%E6%95%B0%E7%9A%84%E6%95%B0%E5%AD%A6%E9%A2%98%2Csin%28%CE%B1%2B%CF%80%2F3%29%3D1%2F4%CE%B1%E2%88%88%28%CF%80%2F6%2C%CF%80%29%E6%B1%82sin%28%CE%B1%29%E7%9A%84%E5%80%BC.%E6%88%91%E8%A7%A3%E5%88%B0sin%28%CE%B1%2B%CF%80%2F3%29%3D1%2F2sin%CE%B1%2B%28%E6%A0%B9%E5%8F%B73%29%2F2cos%3D1%2F4%E8%AF%B7%E8%AE%B2%E6%B8%85%E6%A5%9A)
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一道高中三角函数的数学题,sin(α+π/3)=1/4α∈(π/6,π)求sin(α)的值.我解到sin(α+π/3)=1/2sinα+(根号3)/2cos=1/4请讲清楚
一道高中三角函数的数学题,
sin(α+π/3)=1/4
α∈(π/6,π)
求sin(α)的值.
我解到sin(α+π/3)=1/2sinα+(根号3)/2cos=1/4
请讲清楚
一道高中三角函数的数学题,sin(α+π/3)=1/4α∈(π/6,π)求sin(α)的值.我解到sin(α+π/3)=1/2sinα+(根号3)/2cos=1/4请讲清楚
sin(α+π/3)=1/2sinα+(根号3)/2cosa=1/4
cosa=±√[1-(sina)^2]
sinα+(√3){±√[1-(sina)^2]}=1/2
(sinα-1/2)^2=1-(sina)^2
2(sina)^2-sina-3/4=0
2[(sina)^2-1/2sina+1/16-1/16-3/8]=0
2[(sina)-1/4]^2-7/8=0
sina=7/16+1/4=11/16