AS we saw in the video, the hyperbolic trigonometric functions [cosh(), sinh(t)] are a parametrication of one branch of the unit hyperbola, which has Cartesian equation [cosh(1), sinh (1)] A(1) = 0.5 The familiar circle trigonometric functions [cos(t), sin(t)] are a parametrication of the unit circle, which has Cartesian equation [cos (1), sin (1)] A( 1) - 0.5 In the case of the circle, the area of the circular sector between [1, 0], [0, 0] and [cos (t), sin(t)] is [ E , as we can see because it is of the area of the unit circle. 271 So in both parametrications of the circle and hyperbola, the parameter t corresponds to twice the area under an arc