# Mathematica Trouble: Solving for x in Sinc[x] > (1/1.01)

• Airsteve0
In summary, the conversation is about solving for x in the equation Sinc[x] > (1/1.01) and how to approach it using Mathematica. The user is facing difficulties with the Solve and NSolve commands and is only looking for positive values within the range of 0 and Pi/2. The Wolfram Alpha website provides helpful visualizations and solutions for the equation. The conversation also mentions the Math & Science Software section of the forum for better and quicker answers. A possible solution using FindRoot is also mentioned.
Airsteve0
If anyone on here uses Mathematica maybe you could help me with an issue I am having with computing the following:

Solving for x in: Sinc[x] > (1/1.01)

I am looking only at the positive values and not making any headway with the Solve or NSolve commands. I should also mention that this only makes sense for the angle being between 0 and Pi/2.

Last edited:
This
http://www.wolframalpha.com/input/?i=plot+sinc(x)+for+0+<+x+<+pi/2
shows there will be a single open interval where Sinc[x]>1/1.01 and 0<x<pi/2.

This
http://www.wolframalpha.com/input/?i=solve+sinc(x)==1/1.01+and+x>0
gives you the upper endpoint.

When you know there is a single simple interval for a solution then I would suspect that Mathematica might correctly accept

NSolve[Sinc[x]==1/1.01,x]

to give you that upper endpoint, but unfortunately I cannot verify that for you at the moment.

Note: There is the Math & Science Software section of the forum where many of the small questions about Mathematica syntax might be more quickly and better answered. Poke around several sections below the Math category and you will find it.

In[1]:= FindRoot[Sinc[x]-1/1.01,{x,.25}]

Out[1]= {x->0.244097}

## 1. What does the function Sinc[x] represent?

The Sinc[x] function is a mathematical function that stands for the "sine cardinal" function. It is defined as sin(x)/x and is commonly used in signal processing and Fourier analysis.

## 2. How is the inequality Sinc[x] > (1/1.01) solved for x?

The first step in solving this inequality is to isolate the x term on one side of the equation. This can be done by subtracting (1/1.01) from both sides, giving Sinc[x] - (1/1.01) > 0. Then, using algebraic manipulation and knowledge of the properties of the Sinc function, you can find the range of values for x that satisfy the inequality.

## 3. Is there a specific method or function in Mathematica that can be used to solve this type of inequality?

Yes, Mathematica has a built-in function called Reduce that can be used to solve inequalities. This function takes in an expression and a variable and returns a list of conditions that must be satisfied for the variable to satisfy the expression. In this case, it can be used to solve the inequality Sinc[x] > (1/1.01) for x.

## 4. Can the solution to this inequality be graphically represented?

Yes, the solution to this inequality can be graphically represented by plotting the Sinc[x] and (1/1.01) functions on the same graph and finding the values of x where the Sinc[x] function is greater than the (1/1.01) function. Alternatively, the solution can also be represented by using the RegionPlot function in Mathematica.

## 5. Are there any restrictions on the values of x that can satisfy this inequality?

Yes, since the Sinc[x] function is undefined at x=0, the solution to this inequality will exclude that value. Additionally, the solution may also have restrictions based on the domain of the Sinc[x] function, which is typically the set of all real numbers except for x=0.

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