What is the period of #f(theta) = tan ( ( 3 theta)/4 )- cos ( ( theta)/ 5 ) #?

Answer 1

#20pi#

Period of tan t --> #pi# Period of #tan (3t/4) --> (4pi/3)# Period of #cos (t/5) --> 10pi# Least multiple of 10pi and (4pi/3) is #20pi#

(4pi/3) x 15 --> 20pi 10pi x 2 --> 20pi

Period of f(t) --> #20pi#
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Answer 2

To find the period of the function ( f(\theta) = \tan\left(\frac{3\theta}{4}\right) - \cos\left(\frac{\theta}{5}\right) ), we need to identify the smallest positive value of ( p ) such that ( f(\theta + p) = f(\theta) ) for all ( \theta ).

The period of ( \tan(ax) ) is ( \frac{\pi}{|a|} ), and the period of ( \cos(bx) ) is ( \frac{2\pi}{|b|} ).

For ( \tan\left(\frac{3\theta}{4}\right) ), the period is ( \frac{4\pi}{3} ).

For ( \cos\left(\frac{\theta}{5}\right) ), the period is ( 10\pi ).

The least common multiple (LCM) of ( \frac{4\pi}{3} ) and ( 10\pi ) is ( 20\pi ).

Therefore, the period of ( f(\theta) ) is ( 20\pi ).

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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.

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.

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.

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.

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