# Four intersections?

Geometry Level 4

Charley Brians was playing around with the following 6 trigonometric functions:

• $\sin$
• $\cos$
• $\tan$
• $\cot$
• $\sec$
• $\csc$.

He noticed that, for one of them, if he sets it equal to its hyperbolic counterpart—$\sinh, \cosh, \tanh, \coth, \text{sech},$ or $\text{csch},$ respectively—it intersects at exactly four points.

Assuming that we are only dealing with real numbers, which trig function did he pick?

Inspiration: Brian Charlesworth

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