Simplify the following.
1.(sinθ)/(1+cosθ)-(1-cosθ)/(sinθ)
Find the value of the following by using trigonometric identities.
2.if sinθ=0.8,find the values of cosθ and tanθ.
need steps~
two F.3trigonometric identities QUESTIONS
2008-05-11 1:48 am
回答 (2)
2008-05-11 2:26 am
✔ 最佳答案
1. (sinθ)/(1 cosθ)-(1-cosθ)/(sinθ)= (sinθ)^2/[sinθ(1 cosθ)]-[(1 cosθ)(1-cosθ)]/[sinθ(1 cosθ)
= (sinθ)^2/[sinθ(1 cosθ)]-[(1-cosθ)^2]/sinθ(1 cosθ)
= [(sinθ)^2-1 (cosθ)^2]/sinθ(1 cosθ)
= 0/sinθ(1 cosθ)
= 0
2. (sinθ)^2 (cosθ)^2=1
0.8^2 (cosθ)^2=1
0.64 (cosθ)^2=1
(cosθ)^2=0.36
cosθ=士0.6
tanθ=sinθ/cosθ
tanθ=0.8/0.6
tanθ=4/3
tanθ=sinθ/cosθ
tanθ=0.8/(-0.6)
tanθ= -4/3
參考: my knowledge
2008-05-11 2:21 am
1.(sinθ)/(1+cosθ)-(1-cosθ)/(sinθ)
=[sin2θ-(1-cosθ)(1+cosθ)]/[(sinθ)(1+cosθ)]
=[sin2θ-(1-cos2θ)]/[(sinθ)(1+cosθ)]
=(sin2-sin2θ)/[(sinθ)(1+cosθ)]
=0
2.sinθ=0.8
=8/10
=4/5
cosθ=3/5
tanθ=4/3
=[sin2θ-(1-cosθ)(1+cosθ)]/[(sinθ)(1+cosθ)]
=[sin2θ-(1-cos2θ)]/[(sinθ)(1+cosθ)]
=(sin2-sin2θ)/[(sinθ)(1+cosθ)]
=0
2.sinθ=0.8
=8/10
=4/5
cosθ=3/5
tanθ=4/3
收錄日期: 2021-04-23 20:41:27
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https://hk.answers.yahoo.com/question/index?qid=20080510000051KK02051