Applications of Integration
(cod: P-77-51-12)
Consider a point \(P = (\cosh{t},\, \sinh\, {t})\) in the first quadrant on the hyperbola
\[x^2 - y^2 = 1.\] The area of the pink region in the figure below is equal to:

(cod: P-77-51-12)
Consider a point \(P = (\cosh{t},\, \sinh\, {t})\) in the first quadrant on the hyperbola
\[x^2 - y^2 = 1.\] The area of the pink region in the figure below is equal to:

Congratulations, you got this question right!
What we observed in this exercise clarifies a geometric parallel between trigonometric functions and hyperbolic functions. Indeed, if we take a point \(P = (\cos{t},\,\sin\, {t})\), in the first quadrant, on the trigonometric circle, observe that the area of the pink sector is equal to \(t/2\).
