By using taylor's theorem find the value of cos(54.5)
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cos(47*deg)=cos((45+2)*deg) so use cos(x)=cos(x0)-sin(x0)*(x-x0)-cos(x0)*(x-x0)^2/2+… with x0=45*deg=%pi/4 and x=47*deg so x-x0=2*deg=%pi/90. Then cos(x0)=sin(x0)=sqrt(2)/2 so
cos(47*deg)=cos(45*deg)-sin(45*deg)*%pi/90-cos(45*deg)*(%pi/90)^2/2=
sqrt(2)*(1-%pi/90-%pi^2/16200)/2=.68199
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