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SECTION 2 HYPERBOLIC FUNCTIONS There are another group of trigonometric functions called Hyperbolic Functions. They are defined as follows: Hyperbolic sine: sinhx = 2 Hyperbolic cosine: cosh x . 2 tanh x - siabx = "-0" Hyperbolic tan: cosh * e***** Hyperbolic sec: sech: x - 1 coshe Hyperbolic cosec: esch x - 1 sinhx Hyperbolic cot coth x = tamb* QUESTION 5 (KAPS C.B., A) Evaluate the following integrals, expressing your answers in terms of hyperbolic functions. (a) / coshrux dx (b) / coth x dx (c) f sinhx cosh x dx (d) / sinhn x cosh nx ex (e)] sinh mx cosh nux dx QUESTION 6 (MAPSI B) You recently studied the Pythagorean identities involving cos e and sin 0, tan 0 and sec e, cosec e and cot 0. Develop a Pythagorean identity involving cosh e and sinh 0. Use this to find a relationship between tanh 0 and sech 0. QUESTION 7 (MAPS A) Consider the graph of y = cosh"³x A vertical line cuts the curve at the points A and B. Determine the coordinates of A and B if the tangents to the curve at these two points are perpendicular.

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