Question

What is the limit of the length of a side of a regular polygon that is inscribed in a circle??
HW help

Answer 1

are the sides of the regular polygon allowed to increase

Answer 2

yeah.. it can go up to infinity but the accordance should depend on the radius of the circle somehow

Answer 3

sorry, what do you mean by 'accordance'

Answer 4

The side of a polygon inscribed in a circle is a chord (two points tangent to a circle connected by a line). A chord's length, c, is determined by its central angle, θ, and the radius of the circle, r. This relationship may be written as\[c=2r \sin \frac{ \theta }{ 2 }\]The central angle is determined by the number of sides, n, because each side (or chord) must be equal and must divide the circle into equal segments.\[\theta=\frac{ 360° }{ n }=\frac{ 2\pi }{ n }\]Plug that into the equation for chord length to find an equation representing the length, s, of a side of a regular polygon which has n sides.\[s=2r \sin \frac{ \pi }{ n }\]Then find the limit of the formula as number of sides, n, increases infinitely.\[\lim_{n \rightarrow \infty}2r \sin \frac{ \pi }{ n } = ?\]