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AP CALCULUS PRECALCULUS SUPPLEMENTARY VIII Problems : 1) a) Solve for x : ee xx = 2 3 4 . Hint : Note that e e x x = 1 . Let ue x = and then solve for u . b) There is a special class of exponential functions that have an intimate connection with the hyperbola which is a type of conic ( hyperbola have the Cartesian form x a y b = 22 1 or x a y b =− 1where a and b are positive constants; a rectangular hyperbola takes the form y k x = or y k x where k is a constant). Two such special exponential functions are the hyperbolic sine function , designated by ( ) sinh x (pronounced CINCH x ) and the hyperbolic cosine function , designated by () cosh x (pronounced KOSH x ). The hyperbolic sine function is defined as sinh x = 2 while the hyperbolic cosine function is defined as cosh x = + 2 . Using your calculator, find the exact value of sinh ln2 . Most scientific calculators have a button labelled hyp that must be used with the sin button to activate the hyperbolic sine function. c) Trigonometric functions are the result of the parametric equations xR = cos θ and yR = sin which satisfy the equation of the circle which is another type of conic (circles have the Cartesian form xyR 2 += ). Show by direct substitution of the parametric equations into the Cartesian form of a circle that you get the fundamental trigonometric identity : cos sin 1 θθ .
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This note was uploaded on 07/27/2010 for the course MATH MATH 1025 taught by Professor Tanny during the Spring '09 term at York University.

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