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

In summary, the function csc 4x represents the cosecant of 4 times x, and its period is equal to π/2. This is different from other trigonometric functions because it is the reciprocal of the period of sin 4x. The domain of csc 4x is all real numbers except for values that make the function undefined, and the range is all real numbers except for 0. Csc 4x is related to other trigonometric functions through identities and can be expressed in terms of other functions. Its graph is also a reflection of the graph of sec 4x across the y-axis.
  • #1
karush
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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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  • #2
$y = \csc(Bx)$$T = \dfrac{2\pi}{B} = \dfrac{2\pi}{4} = \dfrac{\pi}{2}$
 
  • #3
Hard to remember stuff like that
my mind freezes at tests alto I got some A's occasionally:unsure:
 

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

1. What is the period of the function csc 4x?

The period of a function is the length of one complete cycle or repetition of the function. In the case of csc 4x, the period is equal to 2π/4, or π/2. This means that the function will repeat itself every π/2 units on the x-axis.

2. How do you find the period of a csc function?

To find the period of a csc function, you can use the formula 2π/b, where b is the coefficient of x in the function. In this case, the coefficient of x is 4, so the period is equal to 2π/4, or π/2.

3. Is the period of csc 4x the same as the period of sin 4x?

Yes, the period of csc 4x is the same as the period of sin 4x. This is because csc and sin are reciprocal functions, meaning that they have the same shape and period, but are reflected across the x-axis.

4. Can the period of a csc function be negative?

No, the period of a function cannot be negative. The period represents a distance on the x-axis, and distance cannot be negative. However, the function itself can have negative values depending on the value of x.

5. How does the period of csc 4x compare to the period of csc x?

The period of csc 4x is shorter than the period of csc x. This is because the coefficient of x in csc 4x is 4, which compresses the function horizontally and causes it to repeat more frequently compared to csc x.

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