Consider a periodic function f(x) with period 2π defined as follows. In the region −π ≤ x ≤ π, define it as f(x) = x , and for all x outside the range −π ≤ x ≤ π define it by the periodicity condition...

Consider a periodic function

f(x)

with period

2π

defined as follows. In the region

−π ≤ x ≤ π
, define it as

f(x) = x

, and for all

x

outside the range

−π ≤ x ≤ π

define it by the periodicity condition

f(x + 2π) = f(x)
.
Sketch a graph of the function then derive expressions for the coefficients
a₀, a_k
and
b_k

in the expansion provided.

Extracted text: ao f (x) = +> (ãk sin(kax)+ ak cos(kx)) k=1 using the formulae T 1 - f(2) cos(ka) dæ - f(x) sin(kæ) dæ ak and - T