解答
sin(66∘−x)368.02=sin(38∘)290
解答
x=−360∘n+66∘−0.89673…,x=−180∘−360∘n+66∘+0.89673…
+1
弧度
x=3011π−0.89673…−2πn,x=−π+3011π+0.89673…−2πn求解步骤
sin(66∘−x)368.02=sin(38∘)290
使用分式交叉相乘
sin(66∘−x)368.02=sin(38∘)290
使用分式交叉相乘: 若 ba=dc 则 a⋅d=b⋅c368.02sin(38∘)=sin(66∘−x)⋅290
368.02sin(38∘)=sin(66∘−x)⋅290
交换两边sin(66∘−x)⋅290=368.02sin(38∘)
两边除以 290
sin(66∘−x)⋅290=368.02sin(38∘)
两边除以 290290sin(66∘−x)⋅290=290368.02sin(38∘)
化简sin(66∘−x)=290368.02sin(38∘)
sin(66∘−x)=290368.02sin(38∘)
验证解
找到无定义的点（奇点）:sin(66∘−x)=0
取 sin(66∘−x)368.02 的分母，令其等于零
sin(66∘−x)=0
以下点无定义sin(66∘−x)=0
将不在定义域的点与解相综合:
sin(66∘−x)=290368.02sin(38∘)
使用反三角函数性质
sin(66∘−x)=290368.02sin(38∘)
sin(66∘−x)=290368.02sin(38∘)的通解sin(x)=a⇒x=arcsin(a)+360∘n,x=180∘−arcsin(a)+360∘n66∘−x=arcsin(290368.02sin(38∘))+360∘n,66∘−x=180∘−arcsin(290368.02sin(38∘))+360∘n
66∘−x=arcsin(290368.02sin(38∘))+360∘n,66∘−x=180∘−arcsin(290368.02sin(38∘))+360∘n
解 66∘−x=arcsin(290368.02sin(38∘))+360∘n:x=−360∘n+66∘−arcsin(290368.02sin(38∘))
66∘−x=arcsin(290368.02sin(38∘))+360∘n
将 66∘到右边
66∘−x=arcsin(290368.02sin(38∘))+360∘n
两边减去 66∘66∘−x−66∘=arcsin(290368.02sin(38∘))+360∘n−66∘
化简−x=arcsin(290368.02sin(38∘))+360∘n−66∘
−x=arcsin(290368.02sin(38∘))+360∘n−66∘
两边除以 −1
−x=arcsin(290368.02sin(38∘))+360∘n−66∘
两边除以 −1−1−x=−1arcsin(290368.02sin(38∘))+−1360∘n−−166∘
化简
−1−x=−1arcsin(290368.02sin(38∘))+−1360∘n−−166∘
化简 −1−x:x
−1−x
使用分式法则: −b−a=ba=1x
使用法则 1a=a=x
化简 −1arcsin(290368.02sin(38∘))+−1360∘n−−166∘:−360∘n+66∘−arcsin(290368.02sin(38∘))
−1arcsin(290368.02sin(38∘))+−1360∘n−−166∘
对同类项分组=−1360∘n−−166∘+−1arcsin(290368.02sin(38∘))
−1360∘n=−360∘n
−1360∘n
使用分式法则: −ba=−ba=−1360∘n
使用法则 1a=a=−360∘n
=−360∘n−−166∘+−1arcsin(290368.02sin(38∘))
−166∘=−66∘
−166∘
使用分式法则: −ba=−ba=−166∘
使用分式法则: 1a=a166∘=66∘=−66∘
−1arcsin(290368.02sin(38∘))=−arcsin(290368.02sin(38∘))
−1arcsin(290368.02sin(38∘))
使用分式法则: −ba=−ba=−1arcsin(290368.02sin(38∘))
使用分式法则: 1a=a1arcsin(290368.02sin(38∘))=arcsin(290368.02sin(38∘))=−arcsin(290368.02sin(38∘))
=−360∘n−(−66∘)−arcsin(290368.02sin(38∘))
使用法则 −(−a)=a=−360∘n+66∘−arcsin(290368.02sin(38∘))
x=−360∘n+66∘−arcsin(290368.02sin(38∘))
x=−360∘n+66∘−arcsin(290368.02sin(38∘))
x=−360∘n+66∘−arcsin(290368.02sin(38∘))
解 66∘−x=180∘−arcsin(290368.02sin(38∘))+360∘n:x=−180∘−360∘n+66∘+arcsin(290368.02sin(38∘))
66∘−x=180∘−arcsin(290368.02sin(38∘))+360∘n
将 66∘到右边
66∘−x=180∘−arcsin(290368.02sin(38∘))+360∘n
两边减去 66∘66∘−x−66∘=180∘−arcsin(290368.02sin(38∘))+360∘n−66∘
化简−x=180∘−arcsin(290368.02sin(38∘))+360∘n−66∘
−x=180∘−arcsin(290368.02sin(38∘))+360∘n−66∘
两边除以 −1
−x=180∘−arcsin(290368.02sin(38∘))+360∘n−66∘
两边除以 −1−1−x=−1180∘−−1arcsin(290368.02sin(38∘))+−1360∘n−−166∘
化简
−1−x=−1180∘−−1arcsin(290368.02sin(38∘))+−1360∘n−−166∘
化简 −1−x:x
−1−x
使用分式法则: −b−a=ba=1x
使用法则 1a=a=x
化简 −1180∘−−1arcsin(290368.02sin(38∘))+−1360∘n−−166∘:−180∘−360∘n+66∘+arcsin(290368.02sin(38∘))
−1180∘−−1arcsin(290368.02sin(38∘))+−1360∘n−−166∘
对同类项分组=−1180∘+−1360∘n−−166∘−−1arcsin(290368.02sin(38∘))
−1180∘=−180∘
−1180∘
使用分式法则: −ba=−ba=−180∘
使用法则 1a=a=−180∘
=−180∘+−1360∘n−−166∘−−1arcsin(290368.02sin(38∘))
−1360∘n=−360∘n
−1360∘n
使用分式法则: −ba=−ba=−1360∘n
使用法则 1a=a=−360∘n
=−180∘−360∘n−−166∘−−1arcsin(290368.02sin(38∘))
−166∘=−66∘
−166∘
使用分式法则: −ba=−ba=−166∘
使用分式法则: 1a=a166∘=66∘=−66∘
−1arcsin(290368.02sin(38∘))=−arcsin(290368.02sin(38∘))
−1arcsin(290368.02sin(38∘))
使用分式法则: −ba=−ba=−1arcsin(290368.02sin(38∘))
使用分式法则: 1a=a1arcsin(290368.02sin(38∘))=arcsin(290368.02sin(38∘))=−arcsin(290368.02sin(38∘))
=−180∘−360∘n−(−66∘)−(−arcsin(290368.02sin(38∘)))
使用法则 −(−a)=a=−180∘−360∘n+66∘+arcsin(290368.02sin(38∘))
x=−180∘−360∘n+66∘+arcsin(290368.02sin(38∘))
x=−180∘−360∘n+66∘+arcsin(290368.02sin(38∘))
x=−180∘−360∘n+66∘+arcsin(290368.02sin(38∘))
x=−360∘n+66∘−arcsin(290368.02sin(38∘)),x=−180∘−360∘n+66∘+arcsin(290368.02sin(38∘))
以小数形式表示解x=−360∘n+66∘−0.89673…,x=−180∘−360∘n+66∘+0.89673…