| Author | Help simple math question |
|---|
tangent 22.5 degree = ?
Poor me dont have money buy caculator >.< |
| 0.414213562 |
| thx :D |
0.4142135623730950488016887242097
i may bw wronge in a diget or two because i wrote it not copy\paste XD |
0.4142135623730950488016887242097
My normal calculator no enough space to key in all of them :-( |
you can do it by hand because 22.5 = 45/2. all you need to know is
sin 45 = cos 45 = sqrt(2)/2 (here 45 are degrees not radians)
then you use tan 22.5 = (sin 22.5)/(cos 22.5) = (sin 45/2) / (cos 45/2)
now you have the identities:
sin 2x = 2 (sin x) * (cos x)
cos 2x = 1 - 2* (sin x) * (sin x)
Set x = 45/2, and you have a system of two equations with two unknowns: (sin x) = (sin 22.5) and (cos x) = (cos 22.5), since you know (sin 2x)=(sin 45) and (cos 2x) = (cos 45).
You solve the system, you obtain sin 22.5 and cos 22.5 and compute the tan 22.5 by their ratio.
Screw the calculators! |
well if you want to use it in a calculation you can just use0.4142
and if you just want to expand your info in math then memorise
0.4142135623730950488016887242097 |
@ naviron
I cannot remember that much after left school sooooo many year :-S |
to naviron:
u wouldn't mind sitting next to me on the test tomorrow would u? >.< |
