解答
sin(2x−10∘)=0.4
解答
x=180∘n+20.41151…+5∘,x=180∘n+90∘+5∘−20.41151…
+1
弧度
x=20.41151…+36π+πn,x=2π+36π−20.41151…+πn求解步骤
sin(2x−10∘)=0.4
使用反三角函数性质
sin(2x−10∘)=0.4
sin(2x−10∘)=0.4的通解sin(x)=a⇒x=arcsin(a)+360∘n,x=180∘−arcsin(a)+360∘n2x−10∘=arcsin(0.4)+360∘n,2x−10∘=180∘−arcsin(0.4)+360∘n
2x−10∘=arcsin(0.4)+360∘n,2x−10∘=180∘−arcsin(0.4)+360∘n
解 2x−10∘=arcsin(0.4)+360∘n:x=180∘n+2arcsin(0.4)+5∘
2x−10∘=arcsin(0.4)+360∘n
将 10∘到右边
2x−10∘=arcsin(0.4)+360∘n
两边加上 10∘2x−10∘+10∘=arcsin(0.4)+360∘n+10∘
化简2x=arcsin(0.4)+360∘n+10∘
2x=arcsin(0.4)+360∘n+10∘
两边除以 2
2x=arcsin(0.4)+360∘n+10∘
两边除以 222x=2arcsin(0.4)+2360∘n+210∘
化简
22x=2arcsin(0.4)+2360∘n+210∘
化简 22x:x
22x
数字相除:22=1=x
化简 2arcsin(0.4)+2360∘n+210∘:180∘n+2arcsin(0.4)+5∘
2arcsin(0.4)+2360∘n+210∘
对同类项分组=2360∘n+2arcsin(0.4)+210∘
2360∘n=180∘n
2360∘n
数字相除:22=1=180∘n
210∘=5∘
210∘
使用分式法则: acb=c⋅ab=18⋅2180∘
数字相乘:18⋅2=36=5∘
=180∘n+2arcsin(0.4)+5∘
x=180∘n+2arcsin(0.4)+5∘
x=180∘n+2arcsin(0.4)+5∘
x=180∘n+2arcsin(0.4)+5∘
解 2x−10∘=180∘−arcsin(0.4)+360∘n:x=180∘n+90∘+5∘−2arcsin(0.4)
2x−10∘=180∘−arcsin(0.4)+360∘n
将 10∘到右边
2x−10∘=180∘−arcsin(0.4)+360∘n
两边加上 10∘2x−10∘+10∘=180∘−arcsin(0.4)+360∘n+10∘
化简2x=180∘−arcsin(0.4)+360∘n+10∘
2x=180∘−arcsin(0.4)+360∘n+10∘
两边除以 2
2x=180∘−arcsin(0.4)+360∘n+10∘
两边除以 222x=90∘−2arcsin(0.4)+2360∘n+210∘
化简
22x=90∘−2arcsin(0.4)+2360∘n+210∘
化简 22x:x
22x
数字相除:22=1=x
化简 90∘−2arcsin(0.4)+2360∘n+210∘:180∘n+90∘+5∘−2arcsin(0.4)
90∘−2arcsin(0.4)+2360∘n+210∘
对同类项分组=90∘+2360∘n−2arcsin(0.4)+210∘
2360∘n=180∘n
2360∘n
数字相除:22=1=180∘n
210∘=5∘
210∘
使用分式法则: acb=c⋅ab=18⋅2180∘
数字相乘:18⋅2=36=5∘
=90∘+180∘n−2arcsin(0.4)+5∘
对同类项分组=180∘n+90∘+5∘−2arcsin(0.4)
x=180∘n+90∘+5∘−2arcsin(0.4)
x=180∘n+90∘+5∘−2arcsin(0.4)
x=180∘n+90∘+5∘−2arcsin(0.4)
x=180∘n+2arcsin(0.4)+5∘,x=180∘n+90∘+5∘−2arcsin(0.4)
以小数形式表示解x=180∘n+20.41151…+5∘,x=180∘n+90∘+5∘−20.41151…