# 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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