It is given that p=ai+j and q=i+aj,where 0 is smaller than a is smaller than 1
(a)Prove that |p| =|q|
(b)If |p| =|p-q|
(1)Find the value of a,and
(2)by finding the value of θ,evaluate tan75° in surd form
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amaths
2008-01-13 5:58 am
回答 (1)
2008-01-13 6:39 am
✔ 最佳答案
(a)|p|=√(a^2+1)
|q|=√(1+a^2)
|p|=|q|
(b)(1)
p-q=(a-1)i+(1-a)j
|p-q|=√[(a-1)^2+(1-a)^2]=(√2)(a-1)
|p| =|p-q|
√(a^2+1)=(√2)(a-1)
a^2+1=2(a-1)^2
a^2+1=2a^2-4a+2
a^2-4a+1=0
a=(4-√12)/2=2-√3
(2)
tanθ=a=2-√3
Since we see that θ+θ+60=90
θ=15
tan15=2-√3
tan75=1/(2-√3)=2+√3
收錄日期: 2021-04-25 16:57:52
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