The hyperbolic functions can be expressed using the exponential function. However how are these related to "hyperbolas"?

Yaretzi Mcconnell

Yaretzi Mcconnell

Answered question

2022-11-13

The hyperbolic functions can be expressed using the exponential function. However how are these related to "hyperbolas"?

Answer & Explanation

ontzeidena8a

ontzeidena8a

Beginner2022-11-14Added 17 answers

Let x=cosh(t) and y=sinh(t). Then as t varies, the point (x,y) moves along the right branch of the hyperbola x 2 y 2 = 1.
Jaiden Elliott

Jaiden Elliott

Beginner2022-11-15Added 4 answers

Consider x=cosh t and y=sinh t.
For t R , The coordinates (x,y) trace the curve x 2 y 2 = 1, which is a hyperbola.
We sometimes call trig functions circular functions for a very similar reason. If x=cos t and y=sin t, the coordinates (x,y) trace a circle.

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