解答
sin(x+60∘)=−0.4
解答
x=−0.41151…+360∘n−60∘,x=180∘+0.41151…+360∘n−60∘
+1
弧度
x=−0.41151…−3π+2πn,x=π+0.41151…−3π+2πn求解步骤
sin(x+60∘)=−0.4
使用反三角函数性质
sin(x+60∘)=−0.4
sin(x+60∘)=−0.4的通解sin(x)=−a⇒x=arcsin(−a)+360∘n,x=180∘+arcsin(a)+360∘nx+60∘=arcsin(−0.4)+360∘n,x+60∘=180∘+arcsin(0.4)+360∘n
x+60∘=arcsin(−0.4)+360∘n,x+60∘=180∘+arcsin(0.4)+360∘n
解 x+60∘=arcsin(−0.4)+360∘n:x=−arcsin(52)+360∘n−60∘
x+60∘=arcsin(−0.4)+360∘n
化简 arcsin(−0.4)+360∘n:−arcsin(52)+360∘n
arcsin(−0.4)+360∘n
arcsin(−0.4)=−arcsin(52)
arcsin(−0.4)
=arcsin(−52)
利用以下特性:arcsin(−x)=−arcsin(x)arcsin(−52)=−arcsin(52)=−arcsin(52)
=−arcsin(52)+360∘n
x+60∘=−arcsin(52)+360∘n
将 60∘到右边
x+60∘=−arcsin(52)+360∘n
两边减去 60∘x+60∘−60∘=−arcsin(52)+360∘n−60∘
化简x=−arcsin(52)+360∘n−60∘
x=−arcsin(52)+360∘n−60∘
解 x+60∘=180∘+arcsin(0.4)+360∘n:x=180∘+arcsin(0.4)+360∘n−60∘
x+60∘=180∘+arcsin(0.4)+360∘n
将 60∘到右边
x+60∘=180∘+arcsin(0.4)+360∘n
两边减去 60∘x+60∘−60∘=180∘+arcsin(0.4)+360∘n−60∘
化简x=180∘+arcsin(0.4)+360∘n−60∘
x=180∘+arcsin(0.4)+360∘n−60∘
x=−arcsin(52)+360∘n−60∘,x=180∘+arcsin(0.4)+360∘n−60∘
以小数形式表示解x=−0.41151…+360∘n−60∘,x=180∘+0.41151…+360∘n−60∘