What is the period of f ( t ) = sin ⁡ ( t 18 ) + cos ⁡ ( t 21 )?

Question

What is the period of   f  (  t  )  =  sin  ⁡  (      t    18    )  +  cos  ⁡  (      t    21    )?

Warkallent8 · Accepted Answer

The periods dor both   sin kt and   cos kt is   2      π    k  Here, the periods of the separate oscillations given by  sin  ⁡  (      t    18    ) and   cos  ⁡  (      t    21    ) are   36  π and   42  π, respectively,For the compounded oscillation f(t), the period is given bythe period   P  =  36  L  π  =  42  M  π , for the least pair of positiveintegers L and M. So,   P  =  252  π , against L = 7 and M = 6.See how it works.  f  (  t  +  252  π  )  =  sin  ⁡  (      t    18    +  14  π  )  +  cos  ⁡  (      t    21    +  12  π  )  =  sin  ⁡  (      t    18    )  +  cos  ⁡  (      t    21    )=f(t)Note that when this P is halved, the first term would change its sign.

ormaybesaladqh · Accepted Answer

Period of   sin  ⁡  (      t    18    )  →  18  (  2  π  )  =  36  πPeriod of   cos  ⁡  (      t    21    )  →  21  (  2  π  )  =  42  πLeast common multiple of   36  π and   42  π  (  36  π  )  ×  (  7  )  →  252  π  (  42  π  )  ×  (  6  )  →  252  πPeriod of   f  (  t  )  →  252  π

What is the period of f(t)=sin(t /18)+cos((t)/21)

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