sin(x+11π/6)=sin(x-π/6)怎么得到的

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sin(x+11π/6)=sin(x-π/6)怎么得到的sin(x+11π/6)=sin(x-π/6)怎么得到的sin(x+11π/6)=sin(x-π/6)怎么得到的sin(x+11π/6)=sin

sin(x+11π/6)=sin(x-π/6)怎么得到的
sin(x+11π/6)=sin(x-π/6)怎么得到的

sin(x+11π/6)=sin(x-π/6)怎么得到的
sin(x+11π/6)=sin(x+2π-π/6),因为2π是一个周期,可以消去,于是得到答案sin(x-π/6)

诱导公式的应用sin(x+2kπ)=sinx,
sin(x+11π/6-2π)=sin(x-π/6)

sin函数曲线,每2π一个周期,

所以sin(x)=sin(x+2π)

同理sin(x-π/6)=sin(x-π/6+2π)=sin(x+11π/6)

根据正弦图像及规律,周期为2π,然后有sint=sin(t+2π),所以sin(x-π/6)=sin(x-π/6+2π),即为sin(x-π/6)=sin(x+11/6π)