Given that tan(90°-θ) = 3/4, find the value of cosθ - sinθ.
我用左好多方法都計唔到, 請好心人教教我.
sin cos tan maths 1條!
2007-04-30 6:55 pm
回答 (5)
2007-04-30 7:19 pm
✔ 最佳答案
tan(90°-θ) = 3/41/tanθ=3/4
cosθ/sinθ=3/4
sinθ=4cosθ/3
cosθ - sinθ=cosθ-4cosθ/3
=cosθ/3
θ=90-tan^-1 3/4
cosθ/3=( 90-tan^-1 3/4)/3
=17.7(corr. to 3 sig.fig.)
2007-05-01 12:59:59 補充：
驀錯機θ=90-tan^-1 3/4,我都計到1/5 θ=53.13
參考: me
2007-05-01 4:57 am
1/ tanθ = 3/4
cosθ/sinθ=3/4
cosθ=3sinθ/4
therefore cosθ - sinθ
=3sinθ/4-sinθ
=3sinθ/4-4sinθ/4
=-sinθ/4
cosθ/sinθ=3/4
cosθ=3sinθ/4
therefore cosθ - sinθ
=3sinθ/4-sinθ
=3sinθ/4-4sinθ/4
=-sinθ/4
參考: myself
2007-05-01 3:38 am
draw a triangle ABC
because tan(90-θ)=3/4,即是對邊=3,鄰邊=4,so 斜邊=5
so cosθ=4/5,sinθ=3/5
so cosθ-sinθ=4/5-3/5
=1/5
because tan(90-θ)=3/4,即是對邊=3,鄰邊=4,so 斜邊=5
so cosθ=4/5,sinθ=3/5
so cosθ-sinθ=4/5-3/5
=1/5
參考: me
2007-04-30 7:26 pm
如果只係0°<θ<90°,只要直接畫個三角形嚟計
let一個角做θ,鄰邊=3x,對邊=4x
=>斜邊=5x(Pyth. theorem)
cosθ=3/5
sinθ=4/5
cosθ - sinθ= -1/5
否則,
cotθ=3/4
tanθ=4/3
tanθ>0,0°<θ<90° or 180°<θ<270°
(tanθ)^2+1=(secθ)^2
secθ=5/3 or -5/3
(cotθ)^2+1=(cscθ)^2
cscθ=5/4 or -5/4
For 0°<θ<90°,
cosθ=3/5
sinθ=4/5
cosθ - sinθ= -1/5
For 180°<θ<270°
cosθ= -3/5
sinθ= -4/5
cosθ - sinθ=1/5
let一個角做θ,鄰邊=3x,對邊=4x
=>斜邊=5x(Pyth. theorem)
cosθ=3/5
sinθ=4/5
cosθ - sinθ= -1/5
否則,
cotθ=3/4
tanθ=4/3
tanθ>0,0°<θ<90° or 180°<θ<270°
(tanθ)^2+1=(secθ)^2
secθ=5/3 or -5/3
(cotθ)^2+1=(cscθ)^2
cscθ=5/4 or -5/4
For 0°<θ<90°,
cosθ=3/5
sinθ=4/5
cosθ - sinθ= -1/5
For 180°<θ<270°
cosθ= -3/5
sinθ= -4/5
cosθ - sinθ=1/5
2007-04-30 7:09 pm
收錄日期: 2021-04-12 21:54:21
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20070430000051KK00980