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

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SUMMARY

The period of the function \( f(x) = \csc{4x} \) is definitively \( \frac{\pi}{2} \). This conclusion is derived from the formula for the period of the cosecant function, which is \( T = \frac{2\pi}{B} \) where \( B \) is the coefficient of \( x \). In this case, \( B = 4 \), leading to \( T = \frac{2\pi}{4} = \frac{\pi}{2} \). Graphical representation supports this finding, confirming the calculated period.

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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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