#### Almeidammiguel

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- Thread starter Almeidammiguel
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You show a right triangle with legs \(\displaystyle 4s\) and \(\displaystyle 5s\) in the picture; I suppose the numbers 4 and 5 could be any integers, which you are calling #1 and #2. Let's call them \(\displaystyle a\) and \(\displaystyle b\) instead, so that in the picture \(\displaystyle a = 4\) and \(\displaystyle b = 5\); and I'll assume that they, too, are given, in addition to length \(\displaystyle s\) and angle \(\displaystyle \theta\).

The expression you wrote becomes \(\displaystyle \frac{as}{\sin(\theta)} - \frac{bs}{\cos(\theta)}\). Can you explain your thinking? Is this supposed to equal x?

One problem I see is that \(\displaystyle a\) and \(\displaystyle b\) will determine \(\displaystyle \theta: \tan(\theta) = \frac{bs}{as} = \frac{b}{a}\). So if \(\displaystyle \theta\) is given, then you are assuming that its tangent is a rational number, which is not true in general. If you knew \(\displaystyle a\) and \(\displaystyle b\), rather than \(\displaystyle \theta\), you could find \(\displaystyle \theta\) from them.

Can you explain the requirements more fully?

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The expression i wrote i was just thinking in how to start the problem! Dont mind it it might not be anything usefull!

You show a right triangle with legs \(\displaystyle 4s\) and \(\displaystyle 5s\) in the picture; I suppose the numbers 4 and 5 could be any integers, which you are calling #1 and #2. Let's call them \(\displaystyle a\) and \(\displaystyle b\) instead, so that in the picture \(\displaystyle a = 4\) and \(\displaystyle b = 5\); and I'll assume that they, too, are given, in addition to length \(\displaystyle s\) and angle \(\displaystyle \theta\).

The expression you wrote becomes \(\displaystyle \frac{as}{\sin(\theta)} - \frac{bs}{\cos(\theta)}\). Can you explain your thinking? Is this supposed to equal x?

One problem I see is that \(\displaystyle a\) and \(\displaystyle b\) will determine \(\displaystyle \theta: \tan(\theta) = \frac{bs}{as} = \frac{b}{a}\). So if \(\displaystyle \theta\) is given, then you are assuming that its tangent is a rational number, which is not true in general. If you knew \(\displaystyle a\) and \(\displaystyle b\), rather than \(\displaystyle \theta\), you could find \(\displaystyle \theta\) from them.

Can you explain the requirements more fully?

The requirement is: if i have a grid of circles and rotate this grid being the rotation center one circle, somewhere there will be a circle that is completly aligned in the axis direction with the circle that serves as rotation centre - Image in attachment.

Thats why i discrimined the tan \(\displaystyle \theta=\frac{a}{b}\) because the grid cannot change!

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