Four intersections?

Geometry Level 4

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

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

He noticed that, for one of them, if he sets it equal to its hyperbolic counterpart—sinh,cosh,tanh,coth,sech,\sinh, \cosh, \tanh, \coth, \text{sech}, or csch,\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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