Trigonometric Deduction from Euler's Formula: Finding the Correct Relations

  • Thread starter Thread starter Hymne
  • Start date Start date
  • Tags Tags
    Trigonometric
Click For Summary
The discussion focuses on deducing the trigonometric identities for cos(a+b) and sin(a+b) using Euler's formula. Participants clarify the correct approach by referencing the relationships between complex exponentials and trigonometric functions. One user initially expresses confusion about their deductions but later realizes their errors were minor. The conversation highlights the importance of verifying calculations in mathematical deductions. Ultimately, the user appreciates the assistance received in resolving their misunderstanding.
Hymne
Messages
87
Reaction score
1
Anybody that can show how to deduce
cos(a+b) = cos(a)cos(b) - sin(a)sin(b)
sin(a+b) = sin(a)cos(b) + sin(b)cos(a)
From the relations that we get from eulers formula..
Should be really simple but I think that I have got some relations wrong so I need to se the real solution.:rolleyes:
Thanks!
 
Mathematics news on Phys.org
Which relations have you got wrong?
 
Your relations are fine. Use this to verify it:

cos(a + b) = Re[cis(a)cis(b)]
sin(a + b) = Im[cis(a)cis(b)]
 
neutrino said:
Which relations have you got wrong?

Hehe it turned out to be that I had it all right I had just made a stupid misstake and was to close to detect it.
Thanks for the help, both of you.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
View full post »

Similar threads

Undergrad Determine ## \beta ## as a function of ##\theta## linkage
  • · Replies 2 ·
Replies
2
Views
2K
Deduce orthogonality relations for sine and cosine w/ Euler's Formula
  • · Replies 1 ·
Replies
1
Views
1K
Alternative deduction of sum of sine and cosine
  • · Replies 2 ·
Replies
2
Views
2K
What is the history and significance of Euler's formula?
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Proof of double angle formulas using Euler's equation
  • · Replies 2 ·
Replies
2
Views
3K
MHB Finding the domain of this function.
  • · Replies 5 ·
Replies
5
Views
2K
How to get the absolute position of a relative object?
  • · Replies 6 ·
Replies
6
Views
3K
Proving Euler's Formula: A Rigorous Approach from First Principles
  • · Replies 15 ·
Replies
15
Views
6K
MHB Factoring exponents from trig functions
  • · Replies 1 ·
Replies
1
Views
3K
Possible complex angles with no imaginary periodicity
  • · Replies 1 ·
Replies
1
Views
2K