How do you solve this equation for A: \sin(5A)+\cos(5A)\sin(A)-\cos(3A)=0

eleticsty5

eleticsty5

Answered question

2022-02-28

How do you solve this equation for A:
sin(5A)+cos(5A)sin(A)cos(3A)=0

Answer & Explanation

Jowiszowy9zb

Jowiszowy9zb

Beginner2022-03-01Added 5 answers

sin(5A)+cos(5A)sin(A)cos(3A)=0
Let x=eiA and use De Moivre's,
x5x52i+x5+x52xx12ix3x32i=0
Multiply by 4ix6,
2(x11x)+(x10+1)(x21)2(x9x3)
=(x21)(x10+2x9+2x+1)=0
The phase of each root to the polynomial above (the ones with |x|=1 at least) is a solution A to your equation (up to an integer addition of 2π).

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?