解答
11sin(x+37.09∘)=1
解答
x=0.30627…+360∘n−37.08999…∘,x=180∘−0.30627…+360∘n−37.08999…∘
+1
弧度
x=0.30627…−1189245π+2πn,x=π−0.30627…−1189245π+2πn求解步骤
11sin(x+37.09∘)=1
两边除以 11
11sin(x+37.08999…∘)=1
两边除以 111111sin(x+37.08999…∘)=111
化简
1111sin(x+37.08999…∘)=111
化简 1111sin(x+37.08999…∘):sin(x+37.08999…∘)
1111sin(x+37.08999…∘)
约分:11=sin(x+37.08999…∘)
化简 111:1111
111
乘以共轭根式 1111=11111⋅11
1⋅11=11
1111=11
1111
使用根式运算法则: aa=a1111=11=11
=1111
sin(x+37.08999…∘)=1111
sin(x+37.08999…∘)=1111
sin(x+37.08999…∘)=1111
使用反三角函数性质
sin(x+37.08999…∘)=1111
sin(x+37.08999…∘)=1111的通解sin(x)=a⇒x=arcsin(a)+360∘n,x=180∘−arcsin(a)+360∘nx+37.08999…∘=arcsin(1111)+360∘n,x+37.08999…∘=180∘−arcsin(1111)+360∘n
x+37.08999…∘=arcsin(1111)+360∘n,x+37.08999…∘=180∘−arcsin(1111)+360∘n
解 x+37.08999…∘=arcsin(1111)+360∘n:x=arcsin(111)+360∘n−37.08999…∘
x+37.08999…∘=arcsin(1111)+360∘n
化简 arcsin(1111)+360∘n:arcsin(111)+360∘n
arcsin(1111)+360∘n
1111=111
1111
使用根式运算法则: na=an111=1121=111121
使用指数法则: xbxa=xb−a11111121=111−211=111−211
数字相减:1−21=21=11211
使用根式运算法则: an1=na1121=11=111
=arcsin(111)+360∘n
x+37.08999…∘=arcsin(111)+360∘n
将 37.08999…∘到右边
x+37.08999…∘=arcsin(111)+360∘n
两边减去 37.08999…∘x+37.08999…∘−37.08999…∘=arcsin(111)+360∘n−37.08999…∘
化简x=arcsin(111)+360∘n−37.08999…∘
x=arcsin(111)+360∘n−37.08999…∘
解 x+37.08999…∘=180∘−arcsin(1111)+360∘n:x=180∘−arcsin(111)+360∘n−37.08999…∘
x+37.08999…∘=180∘−arcsin(1111)+360∘n
化简 180∘−arcsin(1111)+360∘n:180∘−arcsin(111)+360∘n
180∘−arcsin(1111)+360∘n
1111=111
1111
使用根式运算法则: na=an111=1121=111121
使用指数法则: xbxa=xb−a11111121=111−211=111−211
数字相减:1−21=21=11211
使用根式运算法则: an1=na1121=11=111
=180∘−arcsin(111)+360∘n
x+37.08999…∘=180∘−arcsin(111)+360∘n
将 37.08999…∘到右边
x+37.08999…∘=180∘−arcsin(111)+360∘n
两边减去 37.08999…∘x+37.08999…∘−37.08999…∘=180∘−arcsin(111)+360∘n−37.08999…∘
化简x=180∘−arcsin(111)+360∘n−37.08999…∘
x=180∘−arcsin(111)+360∘n−37.08999…∘
x=arcsin(111)+360∘n−37.08999…∘,x=180∘−arcsin(111)+360∘n−37.08999…∘
以小数形式表示解x=0.30627…+360∘n−37.08999…∘,x=180∘−0.30627…+360∘n−37.08999…∘