Do you know an analitical way to obtain the tan 22.5°. Without using a calc
2007-09-06 06:39:19 · 3 answers · asked by logivan_net 3 in Science & Mathematics ➔ Mathematics
tan 45° = 1
1 = ( tan 22.5° + tan 22.5° ) / (1 - tan ² 22.5° )
1 - tan ² 22.5 ° = 2 tan 22.5 °
tan ² 22.5° + 2 tan 22.5 ° - 1 = 0
y ² + 2 y - 1 = 0
y = [ - 2 ± √( 4 + 4) ] / 2
y = [- 2 ± 2√2 ] / 2
y = - 1 ± √ 2
tan 22.5° = - 1 + √2
2007-09-06 07:36:40 · answer #1 · answered by Como 7 · 1⤊ 0⤋
tan22.5=opposite side/adjacent side
I'm not positive, so compare answers.
Oh sorry, I gave you the wrong formula. I was way off.
2007-09-06 13:48:17 · answer #2 · answered by Cham Cham 2 · 0⤊ 0⤋
α = 22.5° = Ï/8
1 = tan(Ï/4) = tan(2α) = 2tan(α)/(1-tan²(α))
1 = 2tan(α)/(1-tan²(α))
(1-tan²(α))= 2tan(α)
tan²(α) + 2tan(α) - 1 = 0
Answer: tan(22.5°) = â2 -1
2007-09-06 13:51:24 · answer #3 · answered by Alexander 6 · 0⤊ 0⤋