Register to reply

Some trigonometric, exponential thing?

by M. next
Tags: exponential, thing, trigonometric
Share this thread:
M. next
#1
Nov3-12, 04:44 AM
P: 378
How can we say:

f(x)=A'sin(kx)+B'cos(kx)

or equivalently

f(x)=Ae[itex]^{ikx}[/itex]+Be[itex]^{-ikx}[/itex]??

How are these two equivalent knowing that e[itex]^{ix}[/itex]=cosx+isinx

I don't get this?
Phys.Org News Partner Science news on Phys.org
Experts defend operational earthquake forecasting, counter critiques
EU urged to convert TV frequencies to mobile broadband
Sierra Nevada freshwater runoff could drop 26 percent by 2100
tiny-tim
#2
Nov3-12, 05:11 AM
Sci Advisor
HW Helper
Thanks
tiny-tim's Avatar
P: 26,148
Hi M. next!
Quote Quote by M. next View Post
How can we say:

f(x)=A'sin(kx)+B'cos(kx)

or equivalently

f(x)=Ae[itex]^{ikx}[/itex]+Be[itex]^{-ikx}[/itex]??

How are these two equivalent knowing that e[itex]^{ix}[/itex]=cosx+isinx

I don't get this?
They won't both be real.

Try Euler's formula
what do you get?
M. next
#3
Nov3-12, 05:44 AM
P: 378
it would be: A(coskx +isinkx)+B(coskx-isinkx)
which's (A+B)coskx+i(A-B)sinkx
.. A'coskx+iB'sinkx
where's did the "i" go?

tiny-tim
#4
Nov3-12, 06:04 AM
Sci Advisor
HW Helper
Thanks
tiny-tim's Avatar
P: 26,148
Some trigonometric, exponential thing?

Quote Quote by M. next View Post
it would be: A(coskx +isinkx)+B(coskx-isinkx)
which's (A+B)coskx+i(A-B)sinkx
so B' = i(A-B)
i told you they won't both be real!
M. next
#5
Nov18-12, 03:11 AM
P: 378
Sorry, i didn't check the site from since, I had some connection difficulties.
So, my final question, can this be done? Is the exponential form an alternative for the known trigonometric one?
And why do I use it? Why not keep it in trigonometric form. I am working on potential wells, free particles and so, if this information would help you answer my question.
tiny-tim
#6
Nov18-12, 04:09 AM
Sci Advisor
HW Helper
Thanks
tiny-tim's Avatar
P: 26,148
Hi M. next!
Quote Quote by M. next View Post
Is the exponential form an alternative for the known trigonometric one?
And why do I use it? Why not keep it in trigonometric form.
Yes, they're equally valid alternatives.
You use cos and sin, or real exponentials, if you're only interested in real solutions,

but you use complex exponentials if you're interested in complex solutions.
M. next
#7
Nov18-12, 04:44 AM
P: 378
Thanks, am grateful


Register to reply

Related Discussions
Integration of exponential and trigonometric forms Calculus & Beyond Homework 10
Is this an ego thing, a dishonesty thing, or a smart thing to do? (concerning grades) Academic Guidance 10
Limit of a trigonometric thing Calculus & Beyond Homework 3
Exponential integral with trigonometric argument Calculus 7
Polynomial, trigonometric, exponential and fractal curves General Math 1