Question

答案这个是怎么算的？详解

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Answer 1

220∠10°-220∠-110°
=220∠10°+220∠(180°-110°)
=220∠10°+220∠70°
|220∠10°+220∠70°|=√[(220cos10°+220cos70°)^2+(220sin10°+220sin70°)^2]
=220√[cos^2(10°)+2cos10°cos70°+cos^2(70°)+sin^2(10°)+2sin10°sin70°+sin^2(70°)]
=220√[1+1+2(cos10°cos70°+sin10°sin70°)]
=220√[2+2cos(70°-10°)]
=220√(2+2×1/2)
=220√3
与x轴正方向的夹角：arctan[(220sin10°+220sin70°)/(220cos10°+220cos70°)]
=arctan[(sin10°+sin70°)/(cos10°+cos70°)]
=arctan{[2sin(70°+10°)/2cos(70°-10°)/2]/[2cos(70°+10°)/2cos(70°-10°)/2]}
=arctan(tan40°)
=40°
∴ 220∠10°-220∠-110°=220√3∠40°