PRECALCULUS SUPPLEMENTARY VIII

PRECALCULUS SUPPLEMENTARY VIII - AP CALCULUS PRECALCULUS...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
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 .
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 3

PRECALCULUS SUPPLEMENTARY VIII - AP CALCULUS PRECALCULUS...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online