2015 Countdown Problem #26: Trig-gy Trigonometry

Geometry Level 4

Consider the following two functions:

\[f(x)=1860\sin(\frac{2\pi x}{2015})\] \[g(x)=775\cos(\frac{2\pi x}{2015})\]

When the graph \(y=f(x)+g(x)\) is plotted against the \(x\) and \(y\) axes, the resulting trigonometric graph has an amplitude of \(\alpha\), a period of \(\beta\) and a y-intercept of \(\gamma\).

Also, the negative \(x\)-intercept of the graph nearest to the \(y\)-axis can be expressed as \(\frac{\sigma}{\pi} \tan^{-1}{\epsilon}\) where \(\sigma\) is an integer.

Determine the value of \[-\frac{\beta\sigma}{\alpha\gamma{\epsilon}^2}\]

This problem is part of the set 2015 Countdown Problems.


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