Euler Formula: Understanding (4.25) to (4.26)

AI Thread Summary
The discussion focuses on the transition from the expression ae^{jwt} + be^{-jwt} to Asin(wt + θ) using Euler's formulas and trigonometric identities. Participants express difficulty in identifying exponents from the uploaded material and inquire about the testing of the upload. Clarification is sought on the application of Euler's formula in this context. Ultimately, one participant confirms their understanding of the conversion process. The conversation highlights the importance of clear notation and effective use of mathematical identities.
pinkcashmere
Messages
17
Reaction score
0
can someone explain how you go from (4.25) to (4.26) using Euler's formulas in the attachment?
 

Attachments

  • Untitled2.png
    Untitled2.png
    4.3 KB · Views: 507
Mathematics news on Phys.org
Although I downloaded and zoomed it I couldn't clearly identify the exponents. Did you test your upload?
 
fresh_42 said:
Although I downloaded and zoomed it I couldn't clearly identify the exponents. Did you test your upload?
Basically, I want to know how you go from
## ae^{jwt}## + ## be^{-jwt}##

to

##Asin(wt + \theta)##
 
ok, i got it now.
thanks
 

Thread 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
View full post »

Thread 'Six Pencil Puzzle'

Is it possible to arrange six pencils such that each one touches the other five? If so, how? This is an adaption of a Martin Gardner puzzle only I changed it from cigarettes to pencils and left out the clues because PF folks don’t need clues. From the book “My Best Mathematical and Logic Puzzles”. Dover, 1994.
View full post »
Thread 'Imaginary Pythagoras'

Thread 'Imaginary Pythagoras'

I posted this in the Lame Math thread, but it's got me thinking. Is there any validity to this? Or is it really just a mathematical trick? Naively, I see that i2 + plus 12 does equal zero2. But does this have a meaning? I know one can treat the imaginary number line as just another axis like the reals, but does that mean this does represent a triangle in the complex plane with a hypotenuse of length zero? Ibix offered a rendering of the diagram using what I assume is matrix* notation...
View full post »

Similar threads

B Getting from complex domain to real domain
Replies
3
Views
1K
Insights Computing the Riemann Zeta Function Using Fourier Series
Replies
5
Views
3K
How to solve this to calculate the input impedance?
Replies
2
Views
1K
A Book to understand Euler angles (and Tait–Bryan )
Replies
1
Views
2K
Using Euler's formula to prove trig identities using "sum to product" technique
Replies
4
Views
2K
B How Does the Unit Circle Relate to Euler's Formula in Complex Numbers?
Replies
10
Views
3K
I Intuitive understanding of Euler's identity?
Replies
6
Views
2K
MHB Proof of Euler's Formula with No Angle Addition
Replies
40
Views
7K
I Extend Euler Product Convergence Over Primes: Basic Qs
Replies
0
Views
1K
MHB Comparing Methods for Initial Value Problem
Replies
38
Views
11K

Hot Threads

Recent Insights

Back
Top