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News Fledglings January 2015 Issue No2 Years t e infoancosancom w wwwancosancom Warm welcome to all our new Fledglings EYEs Managers Geraldine Cray E. 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 1 Fig 92 brPage 6br Version 2 ECE IIT Kharagpur cos cos Fig93pgm k 12 otherwise truncated is if brPage 7br Version 2 ECE IIT Kharagpur 1 1 1 1 1 0 0 0 1 1 1 1 0 0 0 0 1 1 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 If ab be a continuous function and 0 then the area of the region between the graph of and the xaxis is de64257ned to be Area dx Instead of the xaxis we can take a graph of another continuous function such that for all ab and de64257ne the area o a 12 22 a a mn is an arbitrary matrix Rescaling The simplest types of linear transformations are rescaling maps Consider the map on corresponding to the matrix 2 0 0 3 That is 7 2 0 0 3 00 brPage 2br Shears The next simplest type of linear transfo 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 WorksupportedbytheNationalScienceFoundationwhichof3formsatermcantake.Therstformis )sinh()cos( )sinh()sin(.(2)Thesecondformis kysinh(k )sinh()sin( )sin()cos()cos()cos( )sin()sin( M(i)sin1002+sin(i) N(i)cos(i)sin1002A12=NPi=1sin2(i)sin(i)cos(i) (M(i)sin100)2sin(i)cos(i) (N(i)cos(i)sin100)2A13=NPi=1sin(i)cos(i)cos(i) (M(i)sin100)2A22=NPi=1sin(i)sin(i) M( 2(+)cos1 2()cos+cos=2cos1 2(+)cos1 2()coscos=2sin1 2(+)sin1 2()InatriangleABC,a=sinA=b=sinB=c=sinCanda2=b2+c22bccosAPrexesT=tera=1012c=centi=102G=giga=109m=milli=103M=mega=106 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. ) . @x=sincos@ @x=coscos r@ @x=sin rsin@r @y=sinsin@ @y=cossin r@ @y=cos rsin@r @z=cos@ @z=sin rThepositionvectorR=xi+yj+zkiswrittenR=rer:(sphericalcoordinates)IfR=R(t)isaparameterize 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 = . 2011. Together with Families. Hearing Family Stories. Gaining Family Insight. Involving . Family. Naomi Younggren, Ph.D.. 1. Hearing Family Stories. 2. Mass. Health & Human Services . Gaining Family Insight. 5–Minute Check 1. Let (–5, 12) be a point on the terminal side of an. angle . θ . in standard position. Find the exact. values of the six trigonometric functions of . θ. .. Let .