sinθ·cosθ=1/8; 且π/4

来源:学生作业帮助网 编辑:作业帮 时间:2024/11/30 12:09:35
sinθ·cosθ=1/8; 且π/4
xSN@~Kٴ`bbB hTHI$\O51`0 @ض Ӗ4Xp|3|m׌isӓrҵ?MV֏su5 BJ W:oԲaç`xQ>l0MGVHXH*@E>5g~q~VUDNpG- [bZ(ZnъF 4 ۑW):8wD7J9 kKps)# ~M דC+DM®b1ߪr ʿY^ $!/7]/ҁp2 _?q

sinθ·cosθ=1/8; 且π/4
sinθ·cosθ=1/8; 且π/4<θ<π/2 求cosθ-sinθ的值

sinθ·cosθ=1/8; 且π/4
先计算cosθ-sinθ的平方,再开方即可,
(cosθ-sinθ)^2=cos^2+sin^2+2sin cos
=1+2sin cos
=1+1/4=5/4
因为π/4

负的√3/2

先算cosθ-sinθ的平方,再开方
(cosθ-sinθ)^2=cos^2-2sinθ cosθ+sin^2
由公式可知:sin^2+cos^2=1
∴(cosθ-sinθ)^2
=1-2sin θcosθ
有题可知: sinθ·cosθ=1/8
∴ (cosθ-sinθ)^2=3/4
cosθ-sinθ=± √3/2 ...

全部展开

先算cosθ-sinθ的平方,再开方
(cosθ-sinθ)^2=cos^2-2sinθ cosθ+sin^2
由公式可知:sin^2+cos^2=1
∴(cosθ-sinθ)^2
=1-2sin θcosθ
有题可知: sinθ·cosθ=1/8
∴ (cosθ-sinθ)^2=3/4
cosθ-sinθ=± √3/2
∵π/4<θ<π/2∴cos θ<sin θ
∴cosθ-sinθ= -√3/2

收起