# Taylor Series Help: Solving sin(x) Equation

• vucollegeguy
In summary, the conversation discusses the Taylor series of sin(x) and its relationship to the function A*sin(B). The conversation also includes a discussion on factoring out pi/2 and how it relates to the Maclaurin series. The conversation concludes with the individual realizing the solution to their question.
vucollegeguy
The Taylor Series of sin(x)=x-(x3/3!)+(x5/5!)-...

What function of sin gives the following:

($$\pi$$2/(22) - ($$\pi$$4/(24*3!)+ ($$\pi$$6/(26*5!) - ($$\pi$$8/(28*7!)+...

Thank you.

vucollegeguy said:
The Taylor Series of sin(x)=x-(x3/3!)+(x5/5!)-...

What function of sin gives the following:

($$\pi$$2/(22) - ($$\pi$$4/(24*3!)+ ($$\pi$$6/(26*5!) - ($$\pi$$8/(28*7!)+...

Thank you.
Your mix of [ tex] and [ SUP] tags makes it hard to tell what you wrote.

If you factor out pi/2, what do you get?

Thanks.
Got that factored out.

No, your final answer should be something like A*sin(B). Factoring out the pi/2 should give you an idea of what function your Maclaurin series represents.

I don't recogize the series except that it comes from sin(something)...

Isn't this what you have?
$$\frac{\pi}{2}\left(\frac{\pi/2}{1!}~-~\frac{(\pi/2)^3}{3!}~+~\frac{(\pi/2)^5}{5!}~-~\frac{(\pi/2)^7}{7!}~...\right)$$

Looks pretty suggestive to me.

I figured it out as soon as I posted my last reply.
Thanks to you all!

## 1. What is a Taylor Series?

A Taylor Series is a mathematical representation of a function as an infinite sum of terms. Each term in the series is a polynomial function of higher and higher degrees that approximates the original function at a specific point.

## 2. How can Taylor Series help solve a sin(x) equation?

Taylor Series can be used to approximate the value of sin(x) at a specific point by calculating the sum of the terms in the series. This approximation can be used to solve for the value of x in a given sin(x) equation.

## 3. What is the general form of a Taylor Series?

The general form of a Taylor Series is: f(x) = f(a) + f'(a)(x-a) + f''(a)(x-a)^2 / 2! + f'''(a)(x-a)^3 / 3! + ... where f(a) represents the value of the function at the point a, f'(a) represents the first derivative of the function at a, and so on.

## 4. Can Taylor Series be used to solve other types of equations?

Yes, Taylor Series can be used to solve a variety of equations, such as polynomial equations, exponential equations, and trigonometric equations. However, the accuracy of the approximation depends on the number of terms used in the series.

## 5. What is the significance of Taylor Series in mathematics?

Taylor Series is an important tool in mathematics as it allows us to approximate functions and solve equations without relying on complex calculations. It also helps us understand the behavior of a function at a specific point and can be used to prove theorems and solve real-world problems.

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