MathDB

Source: 2017 Canadian Open Math Challenge, Problem C2 —-- A function

f(x)

is periodic with period

T > 0

f(x + T) = f(x)

for all

x

. The smallest such number

T

is called the least period. For example, the functions

\sin(x)

and

\cos(x)

are periodic with least period

2\pi

\qquad

(a) Let a function

g(x)

be periodic with the least period

T = \pi

. Determine the least period of

g(x/3)

\qquad

(b) Determine the least period of

H(x) = sin(8x) + cos(4x)

\qquad

G(x) = sin(cos(x))

and

F(x) = cos(sin(x))

Problem Statement