Without using compound angle formula, calculator and computer,
find the exact value of tan(22.5 degree).
tan(22.5 degree)
2007-05-23 4:44 pm
回答 (4)
2007-05-23 6:01 pm
參考: My Maths knowledge
2007-05-23 10:10 pm
tan45=1
tan(2X22.5)=1
2tan22.5/[1-(tan22.5)^2]=1
2tan22.5=1-(tan22.5)^2
(tan22.5)^2+tan22.5-1=0
設tan22.5=X
X^2+2x-1=0
x=√2-1 或 x=-1-√2(捨去)
therefore,tan22.5=√2-1
tan(2X22.5)=1
2tan22.5/[1-(tan22.5)^2]=1
2tan22.5=1-(tan22.5)^2
(tan22.5)^2+tan22.5-1=0
設tan22.5=X
X^2+2x-1=0
x=√2-1 或 x=-1-√2(捨去)
therefore,tan22.5=√2-1
參考: me
2007-05-23 5:35 pm
http://img411.imageshack.us/img411/9100/anglenp8.jpg
Assume the case as shown in the figure above
tan45°=AC/CD=1
AC^2+CD^2=AD^2(Pyth. thereom)
1^2+1^2=√2
∵∠BAD=∠ADC-∠ABD(ext.∠ of △)
=45°-22.5°=22.5°
∠ABD=∠BAD=22.5°
∴△ABD is isos.△(sides opp. eq.∠s)
BD=AD=√2
tan22.5°=1/ (1+√2)
Assume the case as shown in the figure above
tan45°=AC/CD=1
AC^2+CD^2=AD^2(Pyth. thereom)
1^2+1^2=√2
∵∠BAD=∠ADC-∠ABD(ext.∠ of △)
=45°-22.5°=22.5°
∠ABD=∠BAD=22.5°
∴△ABD is isos.△(sides opp. eq.∠s)
BD=AD=√2
tan22.5°=1/ (1+√2)
2007-05-23 5:06 pm
(Square root 2)-1
You can draw a graph with a square and a rcetangle.
The lenght of the square can let be 1.
The lenghts of the rectangle can let be 1 and Square root 2.
You can draw a graph with a square and a rcetangle.
The lenght of the square can let be 1.
The lenghts of the rectangle can let be 1 and Square root 2.
收錄日期: 2021-04-13 00:31:14
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