Report, edit, etc...Posted by Hofodomo on 2006-03-14 at 18:17:52
Basically, I'm in a "pre-calculus" course (aka functions and trig), and I was just wondering, how do I take the sine of a complex number?
Say, I have sin(a) = 2i (I don't need an actual answer, I just need to figure out the process). How would I go about solving this? Thanks.
Say, I have sin(a) = 2i (I don't need an actual answer, I just need to figure out the process). How would I go about solving this? Thanks.
Report, edit, etc...Posted by BeeR_KeG on 2006-03-14 at 19:45:48
Here's what I'd do:
Sin(a) = 2i
(Sin(a))[sup]2[/sup] = (2i)[sup]2[/sup]
Sin[sup]2[/sup](a) = -4
I think you can keep going.
Sin(a) = 2i
(Sin(a))[sup]2[/sup] = (2i)[sup]2[/sup]
Sin[sup]2[/sup](a) = -4
I think you can keep going.
Report, edit, etc...Posted by Hofodomo on 2006-03-14 at 20:54:28
hmm...i could do that...forgot i^2 = -1 lol
thanks...wait...but now that i have sine squared, how do i isolate the variable?
thanks...wait...but now that i have sine squared, how do i isolate the variable?
Report, edit, etc...Posted by Noober on 2006-03-15 at 15:28:39
Wouldn't the answer be undefined, because there's no value you could take the sine of and get an imaginary number?
Report, edit, etc...Posted by VizuaL on 2006-03-15 at 16:05:35
SOHCAHTOA 
Report, edit, etc...Posted by HolySin on 2006-03-15 at 16:55:58
What variable?
i = (-1)^(0.5)
Are you asking what Sin²x equals? Identity:
(1-Cos2x)/2
Or you could simply start using inverses.
i = (-1)^(0.5)
Are you asking what Sin²x equals? Identity:
(1-Cos2x)/2
Or you could simply start using inverses.
Report, edit, etc...Posted by Noober on 2006-03-15 at 20:45:20
Actually, Sin²x = 1 - Cos²x.
Report, edit, etc...Posted by HolySin on 2006-03-16 at 00:05:23
Actually, if you actually studied my answer and looked at yours, you would realize that they are the same thing.
(1 - Cos2x) / 2 = 1 - Cos²x
(1 - (2Cos²x-1)) / 2 = 1 - Cos²x
(2- 2Cos²x) / 2 = 1 - Cos²x
1 - Cos²x = 1 - Cos²x
(1 - Cos2x) / 2 = 1 - Cos²x
(1 - (2Cos²x-1)) / 2 = 1 - Cos²x
(2- 2Cos²x) / 2 = 1 - Cos²x
1 - Cos²x = 1 - Cos²x
Report, edit, etc...Posted by JordanN_3335 on 2006-03-16 at 09:48:30
All this stuff is boggoling my brain 