tangents Law 如何求角?
本帖最後由 p445hkk20001 於 1-4-2010 01:49 編輯(a + b) / (a - b) = tan((α+β)/2) / tan((α-β)/2)
when I know a,b,α how to know β 本帖最後由 -終場ソ使者- 於 1-4-2010 17:29 編輯
Using compund angle formula
i.e. (a+b)/(a-b)={}/{}
β can be found easily 回復 2# -終場ソ使者-
Using compund angle formula
i.e. (a+b)/(a-b)={}/{[tan(α/ ...
-終場ソ使者- 發表於 1-4-2010 03:27 AM http://www.nakuz.com/bbs/images/common/back.gif
but how can 主項轉換?
if a=8 b=12 α=36.33605751 how to know β? β=117.2796127 (a+b)/(a-b)={}/{}
-5=
-5=tan(α/2)+tan²(α/2)tan(β/2)+tan(β/2)+tan²(β/2)tan(α/2)
Let x,c be tan(β/2),tan(α/2) respectively, (where c is a constant)
-5c+5c²x+5x-5cx²=c+c²x+x+cx²
6cx²-(4+4c²)x+6c=0
x={(4+4c²)±√[(4+4c²)²-4(6c)²]}/2
β=2tan-1x β=2tan-1x
Let x,c be tan(β/2),tan(α/2)
i don't understand .....
when you know β=2tan-1x 即 β=2tan-1 咁又點
so what?
講返我真正目的... 我係想用 知2角 1邊 黎知β
因為我想寫prog ,law of sine 係ASS 會有2個答案 so i really want to know laws of tangents can know the angle? Law of tangents is an extra formula for calculating angles or edges,is useless,meaningless.
In fact,law of sines can have more than one anwers because of SINE.
For example
sin60°=sin120°
can we say 60°=sin-1sin120° ?
The answer is,yes!
Since sinθ=sin(180°-θ) or sinθ=sin(π-θ) 本帖最後由 p445hkk20001 於 2-4-2010 10:14 編輯
做到呢個又點can we say 60°=sin-1sin120° ?
可以代表可以用law tangents 黎求角?
我都知sine law有2個答案
所以睇下tan law 可唔可以求角 算啦,law of tangents係廢架
你想搵兩個solutions用law of sines就夠啦
law of tangents真係好煩,
如果我冇計錯,β應該=2tan-1{{(4+4c²)±√[(4+4c²)²-4(6c)²]}/2}
做到呢個又點can we say 60°=sin-1sin120° ?
可以代表可以用law tangents 黎求角?
呢兩句冇邏輯關係,我只係講law of sines可以有兩個solutions
況且中學既syllabus都冇law of tangents 本帖最後由 p445hkk20001 於 3-4-2010 01:45 編輯
算啦,law of tangents係廢架
你想搵兩個solutions用law of sines就夠啦
law of tangents真係好煩,
如果我冇 ...
-終場ソ使者- 發表於 2-4-2010 11:24 PM http://www.nakuz.com/bbs/images/common/back.gif
我只係在想 方法 解決sine law 的2角答案
β應該=2tan-1{{(4+4c²)±√[(4+4c²)²-4(6c)²]}/2} 唔洗用a,b既資料? 本帖最後由 【YU】 於 3-4-2010 18:28 編輯
真係辛苦晒 -終場ソ使者- 周旋咁耐,仲打埋個derivation俾佢.
sine law 都做倒既野,做咩要將簡單問題複雓化呢.
最重要係得出黎既general formula係一大抽野,有乜用.