In class we discussed the relationship between the hyperbolic functions and a hyperbola then showed that it is analogous to that of the trigonometric functions and a circle. a. Derive an analogue to the Pythagorean Identities (cos2 x + sin2 x- 1, etc. ) for the hyperbolic functions. hint: Which hyperbola and which circ'e? (this will give you the relationship between coshx and sinhx and the others are then easily found as they were in the case of the trigonometric functions, i.e. divide appropriately) b. Use a. to show that the area under the graph offo) = coshx on a bounded interval is equal to the arc length of the same function on the same interval. c. Use the identity in part a. to develop the method of "hyperbolic substitution" (analogous to trigonometric substitution) and use it to evaluate the integral x l m hint: When using trigonometric substitution, it is always a good idea to draw the right triangle since it is then easy to use the Pythagorean theorem and definitions 7 for the trig functions to "see" the correct substitution. Unfortunately, we do not have the luxury of such a familiar geometric interpretation for hyperbolic functions but part a. does give us the algebraic tools necessary