What is the period of f ( t ) = sin ⁡ ( t 18 ) + cos ⁡ ( t 18 )?

For both sin kt and cos kt, the period is 2 π k Here, the periods for the separate oscillations sin ⁡ ( t 18 ) and cos ⁡ ( t 18 ) are the same 36 πAnd so, for the compounded oscillation f ( t ) = sin ⁡ t 18 + cos ⁡ t 18 also the period (= even LCM of separate periods) is the common value 36 π

Question: "What is the period of f ( t..."

Amiya Melendez

Answered question

2022-10-13

What is the period of

f (t) = \sin (\frac{t}{18}) + \cos (\frac{t}{18})

Answer & Explanation

Alannah Yang

Beginner2022-10-14Added 22 answers

For both

\sin

kt and

\cos

kt, the period is

2 \frac{π}{k}

Here, the periods for the separate oscillations

\sin (\frac{t}{18})

and

\cos (\frac{t}{18})

are the same

36 π

And so, for the compounded oscillation

f (t) = \frac{\sin t}{18} + \frac{\cos t}{18}

also the period (= even LCM of separate periods) is the common value

36 π

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