Asked by Jake
Regarding the trigonometric series,
Why does cos start with a 1 and why are the powers of x even numbers
Also for sin, why does sin start with an x and why are the powers odd?
Why does cos start with a 1 and why are the powers of x even numbers
Also for sin, why does sin start with an x and why are the powers odd?
Answers
Answered by
Reiny
You must be referring to the expansion so sinx and cosx
sinx = x - x^3/3! + x^5/5! - x^7/7! + ... and
cosx = 1 - x^2/2! + x^4/4! - x^6/6! ...
I don't know if you have learned about the Taylor Series expansion.
Here is a page that develops the sinx expansion
http://www.intmath.com/Series-expansion/2_Maclaurin-series.php
sinx = x - x^3/3! + x^5/5! - x^7/7! + ... and
cosx = 1 - x^2/2! + x^4/4! - x^6/6! ...
I don't know if you have learned about the Taylor Series expansion.
Here is a page that develops the sinx expansion
http://www.intmath.com/Series-expansion/2_Maclaurin-series.php
Answered by
MathMate
The above reference should help you to answer the questions:
Why does cos start with a 1 and why are the powers of x even numbers
- think of what cos(0) equals, and
- is cos(x) an even or odd function?
Also for sin, why does sin start with an x and why are the powers odd?
- Evaluate lim sin(x)/x as x->0
- Is sin(x) an even or odd function?
Why does cos start with a 1 and why are the powers of x even numbers
- think of what cos(0) equals, and
- is cos(x) an even or odd function?
Also for sin, why does sin start with an x and why are the powers odd?
- Evaluate lim sin(x)/x as x->0
- Is sin(x) an even or odd function?
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.