已知两点A（cos70°,sin70°）,B(cos10°,sin10°),则AB的模长为_数学解答

已知两点A（cos70°,sin70°）,B(cos10°,sin10°),则AB的模长为

人气：497 ℃　时间：2020-06-16 09:09:03

解答

解
AB=√(cos70-cos10)^2+(sin70-sin10)^2
=√cos^2 70+cos^2 10-2cos10cos70+sin^2 70+sin^2 10-2sin10sin70
=√2-2cos10cos70-2sin10sin70
=√2-2(cos10cos70+sin10sin70)
=√2-2×cos(70-10)
=√2-2×1/2
=√2-1
=1