sin cos tan maths 1條!

tan(90°-θ) = 3/4
1/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

1/ tanθ = 3/4
cosθ/sinθ=3/4
cosθ=3sinθ/4
therefore cosθ - sinθ
=3sinθ/4-sinθ
=3sinθ/4-4sinθ/4
=-sinθ/4

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

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

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