作业帮若sin(x+50°)+cos(x+20°)=-√3且x在0到360度中间,0可取,则x的大小.
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若sin(x+50°)+cos(x+20°)=-√3且x在0到360度中间,0可取,则x的大小.
若sin(x+50°)+cos(x+20°)=-√3且x在0到360度中间,0可取,则x的大小.
若sin(x+50°)+cos(x+20°)=-√3且x在0到360度中间,0可取,则x的大小.
sin(x+50°),当X=220°时最小为-1,
cos(x+20°),当X=160°时最小为-1..
那么当X=160°时sin(x+50°)+cos(x+20°)=-1/2+（-1）
【1】∵(x+20)+(70-x)=90.∴x+20=90-(70-x).∴cos(x+20)=cos[90-(70-x)]=sin(70-x).∴sin(x+50)+cos(x+20)=sin(x+50)+sin(70-x)=2sin60cos(x-10)=(√3)cos(x-10)=-√3.∴cos(x-10)=-1.【2】∵0≤x≤360.且cos(x-10)=-1.∴-10≤x-10≤350.∴x-10=180.∴x=190.(单位：度）
sin(x+50°)+cos(x+20°)=sin(x+50°)+sin(70°-x)=2sin60°cos(x-10°）=-√3
故cos(x-10°）=-1/2,所以x-10°=120°，所以x=130°。
-√3=sin(x+50°)+cos(x+20°)=cos(40°-x)+cos(x+20°)=2cos(30°)cos(x-10°) so cos(x-10°)=-1
x=190°
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