a. The expression represents the perimeter of a polygon:
[tex]n\cdot\sin (\frac{360}{2n})[/tex]
n represents the number of sides of the polygon.
b. If we have 60 sides, then n = 60.
We can calculate the approximation given by the expression as:
[tex]\begin{gathered} n\cdot\sin (\frac{360}{2n}) \\ 60\cdot\sin (\frac{360}{2\cdot60}) \\ 60\cdot\sin (\frac{360}{120}) \\ 60\cdot\sin (3) \\ 60\cdot0.0523 \\ 3.138 \end{gathered}[/tex]
We can then calculate the difference with π using a calculator as:
[tex]|3.138-\pi|=0.0036[/tex]
The difference is approximately 0.0036.
