For example.
when x=30,
cos(180+30)= -0.866025...
cos(180-30)= -0.866025...
cos(180+x)= cos(180-x)
Why cos(180+x)= cos(180-x)?
x could be any integer.
Why cos(180+x)= cos(180-x)?
2010-01-25 5:00 am
回答 (2)
2010-01-25 8:09 am
✔ 最佳答案
Proof:cos(180+x)= cos(180-x)
LHD=cos(180+x)
= cos180cosx-sin180sinx
=(-1)cosx-(0)sinx
=-cosx
RHS= cos(180-x)
=cos180cosx+sin180sinx
=(-1)cosx+(0)sinx
=-cosx
therefore cos(180+x)= cos(180-x)
2010-01-25 00:13:57 補充：
cos(180+x)= cos(180-x)
Using the fact cos(360-A) = cosA
cos(180+x)
= cos[360-(180+x)]
= cos(180-x)
2010-01-25 00:14:24 補充：
another method
2010-01-25 5:11 am
Why cos(180+x)= cos(180-x)?
Since cos(180+x) = -cosx [Since 270deg>x>180deg, in qraduant IV]
cos(180-x) = -cosx [Since 180deg >x>90deg , in the quadrant III]
Hence they are equal to each other.
2010-01-24 21:23:32 補充：
我唔太remember 到果個係quadrant幾
但要知道 270deg>x>180deg 時 tan/cot會係正,,,其他負
而 180deg>x>90deg時sin/csc會係正,其他負
因此conclude到兩個quadrant時個value會一樣[suppose x is the same]
2010-01-25 19:32:44 補充：
如果你要simple既話~要畫圖就可以好容易搵到答案
Since cos(180+x) = -cosx [Since 270deg>x>180deg, in qraduant IV]
cos(180-x) = -cosx [Since 180deg >x>90deg , in the quadrant III]
Hence they are equal to each other.
2010-01-24 21:23:32 補充：
我唔太remember 到果個係quadrant幾
但要知道 270deg>x>180deg 時 tan/cot會係正,,,其他負
而 180deg>x>90deg時sin/csc會係正,其他負
因此conclude到兩個quadrant時個value會一樣[suppose x is the same]
2010-01-25 19:32:44 補充：
如果你要simple既話~要畫圖就可以好容易搵到答案
參考: Hope can help you^^”
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原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20100124000051KK01481