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hyperbolics and polar forms

okay i'm just going through some derivations for some homework but i don't understand this line...

We start from here: eiθ=cosθ+isinθ e^{i\theta}= cos \theta + i sin\theta

then: e−iθ=cos(−θ)+isin(−θ) e^{-i\theta}= cos(-\theta) + i sin(-\theta)

and this is apparently equal to:

e−iθ=cosθ−isinθ e^{-i\theta}= cos \theta - isin\theta

now my question is where has the minus gone on the cosine???
Reply 1
Avatar for TeeEm
TeeEm
19
Original post by a10
okay i'm just going through some derivations for some homework but i don't understand this line...

We start from here: eiθ=cosθ+isinθ e^{i\theta}= cos \theta + i sin\theta

then: e−iθ=cos(−θ)+isin(−θ) e^{-i\theta}= cos(-\theta) + i sin(-\theta)

and this is apparently equal to:

e−iθ=cosθ−isinθ e^{-i\theta}= cos \theta - isin\theta

now my question is where has the minus gone on the cosine???


cos(-x) = cosx

even function
Original post by a10
okay i'm just going through some derivations for some homework but i don't understand this line...

We start from here: eiθ=cosθ+isinθ e^{i\theta}= cos \theta + i sin\theta

then: e−iθ=cos(−θ)+isin(−θ) e^{-i\theta}= cos(-\theta) + i sin(-\theta)

and this is apparently equal to:

e−iθ=cosθ−isinθ e^{-i\theta}= cos \theta - isin\theta

now my question is where has the minus gone on the cosine???

A function f is:
even if f(−x)=f(x)f(-x) = f(x),
odd if f(−x)=−f(x)f(-x) = -f(x),
Neither if f(−x)≠±f(x)f(-x) \not= \pm f(x).

cos⁡\cos is even, sinsin is odd.
Reply 3
Avatar for TeeEm
TeeEm
19
EVEN
cos(-x)=cosx
cosh(-x)=coshx


ODD
sin(-x)=-sinx
sinh(-x) =-sinhx

ODD
tan(-x)=-tanx
tanh(-x) =-tanhx

for the rest similar
Reply 4
Avatar for a10
a10
OP
19
Original post by TeeEm
cos(-x) = cosx

even function


Original post by Farhan.Hanif93
A function f is:
even if f(−x)=f(x)f(-x) = f(x),
odd if f(−x)=−f(x)f(-x) = -f(x),
Neither if f(−x)≠±f(x)f(-x) \not= \pm f(x).

cos⁡\cos is even, sinsin is odd.


ahhhhhhhh i forgot this, thanks I got it now :smile:
Reply 5
Avatar for TeeEm
TeeEm
19
Original post by a10
ahhhhhhhh i forgot this, thanks I got it now :smile:


pleasure

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