There are two functions: 1) f ( x ) = cos &#x2061;<!-- ⁡ --> ( n x ) 2)

Reginald Delacruz

Reginald Delacruz

Answered question

2022-06-22

There are two functions:
1) f ( x ) = cos ( n x )
2) f ( x ) = cos ( x )
T = 2 π is the fundamental period of (2) function.
T 1 is the fundamental period of (1) function.
How to prove that T 1 = 2 π n ?

Answer & Explanation

Samantha Reid

Samantha Reid

Beginner2022-06-23Added 22 answers

Use the definition of periodic functions, let T 1 (the smallest non negative real) be the period of the first function so:
f ( x ) = f ( x + T 1 ) ( T 1 0 ) cos n x = cos n ( x + T 1 ) cos n x = cos ( n x + n T 1 ) = cos ( n x + 2 π ) ( I u s e d t h e p e r i o d i c i t y o f t h e s e c o n d f u n c t i o n ) n x + 2 π = n x + n T 1 T 1 = 2 π n

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