Could you show me the workings of this polynomial function f(x)=cos x ?

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1 Answer
Jim G.
Dec 30, 2017

#-(x-pi/2)to(D)#

Explanation:

#"using "color(blue)"Taylor series"#

#•color(white)(x)f(x)=sum_(n=0)^oo(f^n(a))/(n!)(x-a)^n#

#=f(a)+(f'(a))/(1!)(x-a)+(f''(a))/(2!)(x-a)^2+(f'''(a))/(3!)(x-a)^3+...#

#color(orange)"Reminder"#

#d/dx(sinx)=cosx" and "d/dx(cosx)=-sinx#

#"here "a=pi/2#

#f(a)=cos(pi/2)=0#

#f'(x)=-sinxrArrf'(pi/2)=-1#

#"since linear polynomial required we can stop here"#

#rArrf(x)=0+(-1)(x-pi/2)+0#

#rArrf(x)=-(x-pi/2)larrcolor(blue)"linear polynomial"#

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