已知α为锐角,cos(α+30°)=2/3,求sinα=

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已知α为锐角,cos(α+30°)=2/3,求sinα=
已知α为锐角,cos(α+30°)=2/3,求sinα=

已知α为锐角,cos(α+30°)=2/3,求sinα=
cosacos30-sinasin30=2/3
cosa*√3/2=2/3+sina*1/2
两边平方
cos²a*3/4=3/4(1-sin²a)=4/9+2/3*sina+1/4*sin²a
sin²a+2/3sina-11/36=0
sina>0
所以sina=(√15-2)/6

cos(α+30°)=2/3
cosαcos30° -sinα.sin30° =2/3
(√3/2)cosα= 2/3+(1/2)sinα
(3/4)(cosα)^2 = 4/9 + (2/3)sinα + (1/4)(sinα)^2
(sinα)^2 +(2/3)sinα -11/36 =0
36(sinα)^2 +24sinα -11 =0
sinα = (-2+√15)/6