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00 5 00 10 00 15 00 20 00 25 00 30 00 35 00 40 00 50 10 0 1 50 20 0 2 50 30 0 3 50 Ford Fiesta Skoda Fabi Fiat Stil Peugeot 30 Ni ss an Mi cr Ni ss an Tino Op el Cors Ch ry sl er PT Ci tr oen C3 Ford Mondeo Mini Re nault Lagun Peugeot 60 To yo ta Pr. cos eV RF RF RF RF RF RF RF RF RF RF eV eV cos cos cos cos RF RF RF RF RF eV eV eV RF RF RF RF RF RF RF eV eV cos cos cos 66 65 RF RF RF RF RF eV eV cos sin 66 65 5666 566 56 56 566 56 66 65 66 we have that is a second solution of the di64256erential equation 2 and the two solutions and are clearly linearly independent For 8712 we have 0 1 915 1 1 915 1 since 915 1 0 for 0 n This implies that 1 915 1 0 1 915 1 2 1 0 1 91 brPage 1br DERIVATIVE RULES nx dx sin cos dx cos sin dx ln aa dx tan sec dx cot csc dx xgxfxgxgxfx dx cc sec sec tan dx csc csc cot xx dx dfxgxfxfxgx dxgx Theabovecalculationalsoallowsustoobtain~J2,~J2=J2z+1 2(J+J+JJ+)=(jhcos)2+1 2q jh(1+cos)(jh(1cos)+h)q jh(1+cos)q jh(1cos)(jh(1+cos)+h)q jh(1cos)=j(j+1)h2:(25)3.3WaveFunctionsWe MCS320IntroductiontoSymbolicComputationSpring2007[diff(cos(t),t);#differentiationoftheformulacos(t)[diff(cos,t);#wrong![D(cos(t));#alsowrong[D(cos);#differentiationofthecosinefunctionThefollowingi 1+x=1+x=2+O(x2):E(x;l)=E0"cos 2l + lxd 22!+cos 2l + lx+d 22!#=2E0cos2l +2 lx2+d2 4cos2d lxwherewealsousedcos+cos=2cos+ 2cos 2.Theoscillatorydependenceonxofthemeasur WorksupportedbytheNationalScienceFoundationwhichof3formsatermcantake.Therstformis )sinh()cos( )sinh()sin(.(2)Thesecondformis kysinh(k )sinh()sin( )sin()cos()cos()cos( )sin()sin( By the end of today, you should be able to:. Graph the sine and cosine functions. Find the amplitude, period, and frequency of a function. Model Periodic behavior with sinusoids. Unit Circle. The Sine Function: y = . Free Body Diagram. . Lawnmower. Push/Pull. aa. m. g. Force Normal (FN). a. Handle. x. x-axis. Force of Friction (. Ff. ). y. -axis. Forces to consider. Resolve the “Push/Pull” Vector. . Push/Pull (P). (dx0)2+(dy0)2=Z0d0q (1cos0)2+sin20=21 2Z0d0p 1cos0=23 2hp 1+cos0i0=4241s 1+cos 235:Thetotallengthofthependulumis`,thepartthatisstillstraightattimethaslength`,andsothecoordinatesoft Professor Ahmadi. and Robert Proie. Objectives. Learn to Mathematically Describe Sinusoidal Waves. Refresh Complex Number Concepts. Describing a Sinusoidal Wave. Sinusoidal Waves. Described by the equation. AP Calculus BC. Nonhomogeneous Differential Equations. Recall that second order linear differential equations with constant coefficients have the form:. Now we will solve equations where . G. (. x. ) . Jami . Wang. . Period 3. Extra Credit PPT. Pythagorean Identities. sin. 2 . X + cos. 2 . X = 1. tan. 2. X + 1 = sec. 2. X. 1 + cot. 2. X = csc. 2. X. These . identities can be used to help find values of trigonometric functions. . Coefficients. General . Solutions . of NHSOLDE. (Specific Solution). (General Homogeneous Solution). Plug in. (Specific Solution). (General Homogeneous Solution). Plug in. So it is a (General) Solution.