# Four intersections?

Geometry Level 5

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, sech, or csch, respectively--it intersects at exactly four points.

Which trig function did he pick?

Assumption: We are only dealing with real numbers.

Inspiration: Brian Charlesworth

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