How to find the taylor for sin(x)^2 w/ sin(x), is this right?

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In summary, the conversation discusses finding the series representation for sin(x) and how to find the series representation for sin(x)^2. It is determined that the series must be squared in its entirety, including the cross terms, and that this method may be more difficult than finding the series representation for sin(x^2). The conversation concludes with a thank you and goodnight.
  • #1
myusernameis
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Homework Statement



sin(x)= sum((-1)^k* (x^(2k+1)/(2k+1)!))k=0 to infinity

Homework Equations



so if i want to find sin(x)^2, (not sin(x^2), that would be easier though...)

The Attempt at a Solution


then...
do i square the whole thing, like this?

sum(((-1)^k* (x^(2k+1)/(2k+1)!))^2)k=0 to infinity

thanks a bunch!
 
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  • #2
You have to square the whole series (x-x^3/3!+x^5/5!-...)*(x-x^3/3!+x^5/5!-...). It's not just the sum of the squares of each term. It's a double sum. There are cross terms. It's easy enough to find the first few terms that way.
 
  • #3
Dick said:
You have to square ... that way.

ahhh thanks for answering both of my questions!

good night!
 

Related to How to find the taylor for sin(x)^2 w/ sin(x), is this right?

1. What is the Taylor series for sin(x)^2?

The Taylor series for sin(x)^2 is (1/2) - (1/2)cos(2x).

2. How do I find the Taylor series for sin(x)^2?

To find the Taylor series for sin(x)^2, you can use the formula for the Taylor series expansion of a function. In this case, you would need to take the derivatives of sin(x)^2 and evaluate them at x = 0. Then, you can plug these values into the formula to get the Taylor series.

3. Why do we use the Taylor series for sin(x)^2?

The Taylor series for sin(x)^2 is useful for approximating the value of sin(x)^2 for any value of x. It allows us to break down a complex function into simpler terms, making it easier to calculate and understand.

4. Is this the correct Taylor series for sin(x)^2?

Yes, the Taylor series for sin(x)^2 is (1/2) - (1/2)cos(2x). However, it is important to note that the Taylor series is an infinite series and can be approximated to a certain degree depending on the number of terms used.

5. Can the Taylor series for sin(x)^2 be used for other trigonometric functions?

Yes, the Taylor series can be used for other trigonometric functions as well. However, the specific formula and number of terms may vary depending on the function. It is important to understand the principles of Taylor series in order to apply it to other functions.

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