formulas_sheetw - You may find some of the following...

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Unformatted text preview: You may find some of the following formulas useful (but probably not all of them) sin2 (x) + cos2 (x) = 1 and cos(2x) = cos2 (x) - sin2 (x) sin(2x) = 2 sin(x) cos(x) and sin2 (x) = cos2 (x) = 1 + cos(2x) 2 1 - cos(2x) 2 cos(/3) = 1/2 and sin(/3) = 3/2. cos(/4) = 2/2 and sin(/4) = 2/2. cos(/6) = 3/2 and sin(/6) = 1/2. cos(0) = 1 and sin(0) = 0. d dx d dt d d d dr csc(x) = - csc(x) cot(x). sec(t) = sec(t) tan(t). tan() = sec2 (). cot(r) = - csc2 (r). t Arc length function: Length of curve from (x(), y(), z()) to (x(t), y(t), z(t)) is s(t) = T(t) = r (t) |r (t)| |r (u)|du. , N(t) = b, T (t) |T (t)| , B(t) = T(t) N(t) . ba |b| projb a = ba |b|2 compb a = i j k a, b, c d, e, f = det a b c = bf - ce, -(af - cd), ae - bd . d e f a b = -b a , a (b) = (a) b = (a b). (t)) , d (r(t) dt d (r(t) u(t)) = (r (t) u(t)) + (r(t) u dt d (f (t)r(t)) = (f (t)r(t)) + (f (t)r (t)). dt u(t)) = (r (t) u(t)) + (r(t) u (t)) , 2 Second derivative test: D = fxx fyy - fxy . 1 ...
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This note was uploaded on 02/08/2012 for the course MATH 215 at University of Michigan-Dearborn.

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