Too much brute force can kill you!

Geometry Level 5

ξ=sin0+sinϕn+sin2ϕn++sin(n1)ϕn+sinϕcos0+cosϕn+cos2ϕn++cos(n1)ϕn+cosϕ\large{\xi=\frac{\sin0^\circ+\sin\frac{\phi}{n}+\sin\frac{2\phi}{n}+\cdots+\sin\frac{(n-1)\phi}{n}+\sin\phi}{\cos0^\circ+\cos\frac{\phi}{n}+\cos\frac{2\phi}{n}+\cdots+\cos\frac{(n-1)\phi}{n}+\cos\phi}}

The above ratio can be expressed in a simplified form. You may want to find that form first.

If n=71n=71 and ϕ=71\phi=71^\circ, then what is the value of ξ\xi?

Give your answer to three decimal places.

×

Problem Loading...

Note Loading...

Set Loading...