Inextricably Linked: A Trigonometric Coupling
Taylor & Francis
Original Item ID
Inspired by the classroom capsule and its follow-up, we present direct geometric derivations of the integral formulas for both the inverse hyperbolic and inverse polar trig functions, the latter being a new approach independent of Insel’s work. In so doing, we show that these two trigonometric settings are linked in a natural analytical geometric way, establishing a coordinate system determined by hyperbolas that is akin to polar coordinates. We then use the integral formulas to obtain the derivatives of the various hyperbolic and polar trig functions.
Engbers, John; Hammett, Adam; and Hogan, Ian, "Inextricably Linked: A Trigonometric Coupling" (2020). Mathematical and Statistical Science Faculty Research and Publications. 128.