1. If tanθ=0.5, find the values of sinθ,cosθand cos² θ-sin² θ.
列式.
F3 三角比 急.要TEST
2009-10-10 5:41 am
回答 (3)
2009-10-10 6:52 am
✔ 最佳答案
1. If Tanθ=0.5，find the values of Sinθ，Cosθand Cos^2 θ－Sin^2 θ.
Sol
Tanθ=0.5>0
=>θ在第1象限或θ在第3象限
(1) θ在第1象限
Tanθ=0.5=1/2
Sinθ=1/sqrt(5)
Cosθ=2/sqrt(5)
Cos^2 θ－Sin^2 θ=4/5－1/5=3/5
(2) θ在第3象限
Sinθ=－1/sqrt(5)
Cosθ=－2/sqrt(5)
Cos^2 θ－Sin^2 θ=4/5－1/5=3/5
2009-10-10 6:48 am
Should be 3/5 intead of -4/5
2009-10-10 6:04 am
tanθ=0.5=1/2
=>(sinθ)/(cosθ)=1/2
=>sinθ:cosθ=1:2
let sinθ=k and cosθ=2k ,
cos^2θ+sin^2θ=1
=>(k)^2+(2k)^2=1
=>k=1/sqrt(5)
so sinθ=1/sqrt5 and cosθ=2/sqrt5
=>sin^2θ-cos^2θ=(1/sqrt5)^2-(2/sqrt5)^2=-4/5//
=>(sinθ)/(cosθ)=1/2
=>sinθ:cosθ=1:2
let sinθ=k and cosθ=2k ,
cos^2θ+sin^2θ=1
=>(k)^2+(2k)^2=1
=>k=1/sqrt(5)
so sinθ=1/sqrt5 and cosθ=2/sqrt5
=>sin^2θ-cos^2θ=(1/sqrt5)^2-(2/sqrt5)^2=-4/5//
收錄日期: 2021-04-23 23:21:29
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