这个三角函数方程怎么解 x等于多少度 在没有电脑情况下 只有一个计算器 能解出来吗

2025-03-16 11:02:12
推荐回答(1个)
回答(1):

可以解出:
0.1454/(sin50cosx-sinxcos50)=(tanx-tan9)/(sinxcos51+sin51cosx)
0.1454(sinxcos51+sin51cosx)=(sin50cosx-sinxcos50)(tanx-tan9)
0.1454sinxcos51+0.1454sin51cosx=sin50sinx-sin50tan9cosx-sinxtanxcos50+sinxcos50tan9
两边乘以cosx:
0.1454sinxcosxcos51+0.1454sin51cos²x=sin50sinxcosx-sin50tan9cos²x-sin²xcos50+sinxcosxcos50tan9
将sinxcosx化成0.5sin2x, cos²x=(1+cos2x)/2, sin²x=(1-cos2x)/2
则上述方程可化简为:asin2x+bcos2x=c
从而得√(a²+b²)sin(2x+p)=c, 其中p=arctan(b/a)
从而sin(2x+p)=c/√(a²+b²)
即可得x.

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