MHB ACT.trig.01 What is the period of the function csc 4x

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The period of the function f(x) = csc(4x) is determined using the formula T = 2π/B, where B is the coefficient of x. In this case, B equals 4, leading to a period of T = 2π/4 = π/2. Observational methods and graphing confirm this result, as the function exhibits periodic behavior with a period of π/2. Some participants express difficulty in remembering such formulas during tests, despite achieving good grades occasionally. Understanding the relationship between the function's coefficient and its period can aid in retention and application.
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$\tiny{ACT.trig.01}$
What is the period of the function $f(x)=\csc{4x}$
$a. \pi \quad b, 2\pi \quad c. 4\pi \quad d. \dfrac{\pi}{4} \quad e. \dfrac{\pi}{2}$

well we should know the answer by observation
but I had to graph it
looks like $\dfrac{\pi}{2}$
 
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$y = \csc(Bx)$$T = \dfrac{2\pi}{B} = \dfrac{2\pi}{4} = \dfrac{\pi}{2}$
 
Hard to remember stuff like that
my mind freezes at tests alto I got some A's occasionally:unsure:
 

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