There are another group of trigonometric functions called Hyperbolic Functions. They are defined as follows:
cosh x .
tanh x - siabx =
sech: x -
esch x - 1
coth x =
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
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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