Can you please explain to me clearly how to arrive to the general solution for the following?
1. sin (2x-60)=1
2. sin (2x-60) = -1
Thanks a lot!
PS. I am really bad at general solutions. Do you have any good recommendations as to what exercise I can try?
A Math General Solutions
2008-04-15 1:55 am
回答 (2)
2008-04-15 4:06 am
✔ 最佳答案
ｓｉｎ（２ｘ－６０）＝１首先諗ｓｉｎ咩角先等於１（－９０＜＝角＜＝９０）
好明顯，ｓｉｎ９０＝１
而ｓｉｎ既ｇｅｎｅｒａｌ ｓｏｌｕｔｉｏｎ 係 １８０ｎ＋（－１）^ｎ（角)
所以，刪ｓｉｎ，將１轉做個舊野
２ｘ－６０＝１８０ｎ＋（－１）^ｎ（９０）
２ｘ＝１８０ｎ＋（－１）^ｎ（９０）＋６０
ｘ＝９０ｎ＋（－１）^ｎ（４５）＋３０
ｓｉｎ（２ｘ－６０）＝－１
由於ｓｉｎ（－９０）＝－１
２ｘ－６０＝１８０ｎ＋（－１）^ｎ（－９０）
ｘ＝９０ｎ－（－１）^ｎ（４５）＋３０
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2008-04-15 6:34 am
1. sin(2x-60˚)=1
2x-60˚=180n˚+(-1)n(90˚)
2x=180n˚+(-1)n(90˚)+60˚
x=90n˚+(-1)n(45˚)+30˚
2.sin(2x-60˚)=-1
2x-60˚=180n˚+(-1)n(-90˚)
2x=180n˚+(-1)n+1(90˚)+60˚
x=90n˚+(-1)n+1(45˚)+30˚
2008-04-14 22:40:15 補充：
where n is any integer.
2x-60˚=180n˚+(-1)n(90˚)
2x=180n˚+(-1)n(90˚)+60˚
x=90n˚+(-1)n(45˚)+30˚
2.sin(2x-60˚)=-1
2x-60˚=180n˚+(-1)n(-90˚)
2x=180n˚+(-1)n+1(90˚)+60˚
x=90n˚+(-1)n+1(45˚)+30˚
2008-04-14 22:40:15 補充：
where n is any integer.
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原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20080414000051KK01641