已知sinx=-1/3,x∈(-π,-π/2)则X可表示为A.arcsin1/3 B.-π/2-arcsin(-1/3) C.-π+arcsin(-1/3) D.-π-arcsin(-1/3)

来源:学生作业帮助网 编辑:作业帮 时间:2024/11/20 18:48:04
已知sinx=-1/3,x∈(-π,-π/2)则X可表示为A.arcsin1/3 B.-π/2-arcsin(-1/3) C.-π+arcsin(-1/3) D.-π-arcsin(-1/3)
x){}K3*lu u*uthob}#ͧ3#p%娗X T TV iTp jPT$j3X/Hlt3ulHV

已知sinx=-1/3,x∈(-π,-π/2)则X可表示为A.arcsin1/3 B.-π/2-arcsin(-1/3) C.-π+arcsin(-1/3) D.-π-arcsin(-1/3)
已知sinx=-1/3,x∈(-π,-π/2)则X可表示为
A.arcsin1/3 B.-π/2-arcsin(-1/3) C.-π+arcsin(-1/3) D.-π-arcsin(-1/3)

已知sinx=-1/3,x∈(-π,-π/2)则X可表示为A.arcsin1/3 B.-π/2-arcsin(-1/3) C.-π+arcsin(-1/3) D.-π-arcsin(-1/3)
选D
∵arcsinx的值域在(-π/2,π/2)
∴arcsinx(-1/3)∈(-π/2,0)
∵sinx=sin(x+2kπ),且sinx=sin(π-x)
∴sinx=sin(π-x-2π)=sin(-π-x-2π)
∵x∈(-π,-π/2)
∴-x∈(π/2,π)
-π-x∈(-π/2,0)
∴x=-π-arcsinx(-1/3)

D

D

∵arcsinx的值域在(-π/2,π/2)
∴arcsinx(-1/3)∈(-π/2,0)
由已知 X在第三象限而arcsinx(-1/3)在第四象限
所以用π和arcsinx(-1/3)表示X
即得结果D