灵鹊做题网解方程 sinx=3siny x+y=120°
来源：学生作业帮 编辑：灵鹊做题网作业帮 分类：数学作业 时间：2024/04/28 16:21:42
解方程 sinx=3siny x+y=120°
sin(120-y)=3sin(y)
sin120cosy-sinycos120=3siny
√3/2 cosy+1/2siny=3siny
√3/2 cosy=5/2siny
√3/5=tany
y=19.1° x=100.9° h或者sinx=sin(120°-y)=sin120°cosy-cos120°siny=(根号3)(cosy)/2+(siny)/2=3siny
得(根号3)(cosy)/2=5(siny)/2
两边同时平方化简得3cos²y=25sin²y
带入cos²y+sin²y=1
得28sin²y=3,28cos²y=25
sin120cosy-sinycos120=3siny
√3/2 cosy+1/2siny=3siny
√3/2 cosy=5/2siny
√3/5=tany
y=19.1° x=100.9° h或者sinx=sin(120°-y)=sin120°cosy-cos120°siny=(根号3)(cosy)/2+(siny)/2=3siny
得(根号3)(cosy)/2=5(siny)/2
两边同时平方化简得3cos²y=25sin²y
带入cos²y+sin²y=1
得28sin²y=3,28cos²y=25
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