Please show all steps Thanks Find the Taylor polynomial of o

Please show all steps! Thanks! Find the Taylor polynomial of orders 0, 1, 2, and 3 generated by f at a. f(x) = cos x, a = 2pi/3

Solution

y= f(x,y) = cosx

y(2pi/3) = cos(2pi/3) = -1/2

y\' = -sinx

y\'\'= -cosx

y\'\'\' = sinx


so y = -1/2 + (x-2pi/3) (-3/2) + (x-2pi/3)² (1/8) + (x-2pi/3)³ (3)/16