Answered By Leonardo F

We can use the following funtion formula to guide us in this exercise, in which a, b, c and d are constants:

 $y=a\times csc\left(bx-c\right)+d$y=a×csc(bx−c)+d 

Since the cosecant is the inverse of the sine function, the way we calculate the period is the same but, in the case of the cosecant, we cannot calculate the amplitude, because there are no values of maximum and minimum.

To find the period of the function (P), we can use the following formula:

    $P=\frac{2\pi}{b}=\frac{2\pi}{\frac{1}{10}\pi}=20$P=2πb =2π110 π =20 

Since the b value in this example is  $\frac{1}{10\pi}$110π  , the period is 20.

To find out the value of the horizontal phase shift (HFS), we can do:

  $HFS=\frac{c}{b}=\frac{11}{\frac{1}{10}\pi}=\frac{110}{\pi}$HFS=cb =11110 π =110π  

Since, in the function, we are subtracting 11 inside the cosecant, we are shifting the graph of the cosecant to the right by a value of  $\frac{110}{\pi}$110π  . If we approximate the value of  $\pi$π in the calculator, the horizontal phase shift is roughly 35.

In summary, the period of the function is 20 and the horizontal phase shift is exactly  $\frac{110}{\pi}$110π  or approximately 35.