Question

问一道很简单的高一数学题～

若x为锐角，且sin(x-∏/6)=1/3，则cosx的值为_____
求详细过程。。。

Answer 1

x为锐角，则0<x<π/2，则-π/6<x-π/6<π/3

又因为sin(x-π/6)=1/3>0，故0<x-π/6<π/3，故cos(x-π/6)>0，故cos(x-π/6)=(2根号2)/3

cosx=cos[(x-π/6)+π/6]=cos(x-π/6)cos(π/6)-sin(x-π/6)sin(π/6)=(2根号6-1)/6

Answer 2

x为锐角，则0<x<π/2，则-π/6<x-π/6<π/3

又因为sin(x-π/6)=1/3>0，故0<x-π/6<π/3，故cos(x-π/6)>0，故cos(x-π/6)=(2根号2)/3

cosx=cos[(x-π/6)+π/6]=cos(x-π/6)cos(π/6)-sin(x-π/6)sin(π/6)=(2根号6-1)/6

Answer 3

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