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, sech, or 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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