General Sine and Cosine formula for sum of a finite number of angles I was wondering is there is

Babenzgs

Babenzgs

Answered question

2022-01-27

General Sine and Cosine formula for sum of a finite number of angles
I was wondering is there is a general formula for sin(x1+x2+x3++xn) as well as for the cosine function. I know that sin(x1+x2)=sin(x1)cos(x2)+cos(x1)sin(x2) and cos(x1+x2)=cos(x1)cos(x2)sin(x1)sin(x2) But I want to find a general formula for the sum of a finite number of angles for the Sine and the cosine but I didn't noticed any pattern. I suspect that it may have a recursive pattern.

Answer & Explanation

Deegan Mullen

Deegan Mullen

Beginner2022-01-28Added 12 answers

Well, for n=3:
cos(x+y+z)=cos(x+y)cos(z)sin(x+y)sin(z)=(cos(x)cos(y)sin(x)sin(y))cos(z)(sin(x)cos(y)+cos(x)sin(y))sin(z)
It should be easy to do this for higher n as well, and for sin(x+y+z)

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?