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What is the period of #f(theta)= sin 7 t - cos 5 t #?

Answer 1

#2pi#

Period of sin (7t) --> #(2pi/7)# Period of cos (5t) --> #(2pi/5)# Least common multiple of #(2pi)/7# and #(2pi)/5# --> #2pi#

#((2pi)/7)# x (7) --> #2pi# #((2pi)/5)# x (5) --> #2pi#

Answer: Period of f(t) --> #2pi#

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Answer 2

Elijah Alexander

To find the period of ( f(\theta) = \sin(7t) - \cos(5t) ), first identify the periods of the component functions. The period of ( \sin(7t) ) is ( \frac{2\pi}{7} ), and the period of ( \cos(5t) ) is ( \frac{2\pi}{5} ).

The period of the combined function ( f(\theta) ) is the least common multiple (LCM) of the periods of the component functions.

The LCM of ( \frac{2\pi}{7} ) and ( \frac{2\pi}{5} ) is ( \frac{2\pi}{\text{LCM}(7, 5)} ).

The least common multiple of 7 and 5 is 35. Therefore, the period of ( f(\theta) ) is ( \frac{2\pi}{35} ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.