已知 sin[(x/2)-(π/4)]=-(1/4),求x的值。

熱心網(wǎng)友

1.若sinx=a,-1≤a≤1，則x=(-1)^k*arcsina+kπ2.若cosx=a,-1≤a≤1，則x=2kπ±arccosa3.若tanx=a,-1≤a≤1，則x=kπ+arctanasin[(x/2)-(π/4)]=-(1/4), (x/2)-(π/4)=(-1)^k*arcsin（-1/4）+kπ又∵arcsin（-1/4）=π-arcsin(1/4)∴x=2kπ＋[2（－1）^(k+1)] *arcsin(1/4)+(π/2)

熱心網(wǎng)友

sinx=a(0x/2-Pi/4=kPi+(-1)^k*arcsin(-1/4)---x/2=kPi-(-1)^k*arcsin(1/4)+Pi/4---x=2kPi+(-1)^(k+1)*arcsin(1/4)+Pi/2(k∈Z)

熱心網(wǎng)友

sin[(x/2)-(π/4)]=sin(x/2)cos(π/4)-cos(x/2)sin(π/4) =[(√2)/2]sin(x/2)-[(√2)/2]cos(x/2) =[(√2)/2][sin(x/2)-cos(x/2)] =-(1/4)(1/2)[sin^2(x/2)-2sin(x/2)cos(x/2)+cos^2(x/2)]=1/16(1/2)[1-2sin(x/2)cos(x/2)]=(1/16)1-2sin(x/2)cos(x/2)=(1/8)1-sinx=1/8sinx=7/8x=arcsin(7/8)=61°3\'[(x/2)-(π/4)]是第三象限或第四象限的角

熱心網(wǎng)友

已知 sin[(x/2)-(π/4)]=-(1/4),求x的值。解：因為sin[(x/2)-(π/4)]=-(1/4),|-1/4|<1,所以，(x/2)-(π/4)=2kπ+arcsin(-1/4)或(x/2)-(π/4)=(2k+1)π-arcsin(-1/4),(k為整數(shù))即x1=4kπ+2arcsin(-1/4)+π/2,x2=(4k+2)π-2arcsin(-1/4)+π/2,(k為整數(shù)).所以，x1=2nπ+π/2-2arcsin(1/4),x2=2(n+1)π+π/2+2arcsin(1/4),(n為整數(shù)).

熱心網(wǎng)友

sin[(x/2)-(π/4)]=-(1/4)= x/2-pi/4 = arcsin(-1/4) + 2kpi= x = (4k+1/2)pi + arcsin(-1/4)

熱心網(wǎng)友

sin[(x/2)-(π/4)]=sin(x/2)cos(π/4)-cos(x/2)sin(π/4) =(√2)/2[sin(x/2)-cos(x/2)]=-(1/4) [sin(x/2)-cos(x/2)]^2=1/8 sin(x/2)^2+cos(x/2)^2=1 [sin(x/2)-cos(x/2)]^2=sin(x/2)^2+cos(x/2)^2-2sin(x/2)cos(x/2) =1/8 2sin(x/2)cos(x/2)=1-1/8=7/8 又知2sin(x/2)cos(x/2)=sinx=7/8 所以 x=arcsin(7/8)