(a) Let P(cos t, sin t) be a point on the unit circle x² + y² =1 in the first quadrant (see figure). Show that t is equal to twice the area of the shaded circular sector AOP.

(b) Let P(cosh t, sinh t) be a point on the unit hyperbola x² - y² = 1 in the first quadrant (see figure). Show that t is equal to twice the area of the shaded region AOP. Begin by showing that the area of the shaded region AOP is given by the formula

1 y 0 Figure for part (a) P A(1, 0)