use the following graph to obtain the graph of the function found by replacing sin with its reciprocal…

use the following graph to obtain the graph of the function found by replacing sin with its reciprocal function. give the equation of the function for the graph that you obtain.\nwhat is the equation of the reciprocal function?\n( y=square )\n(type an expression using ( x ) as the variable. use integers or fractions for any numbers in the expression.)

use the following graph to obtain the graph of the function found by replacing sin with its reciprocal function. give the equation of the function for the graph that you obtain.\nwhat is the equation of the reciprocal function?\n( y=square )\n(type an expression using ( x ) as the variable. use integers or fractions for any numbers in the expression.)

Answer

Explanation:

Step1: Identify the original function

The original function is ( y = -\frac{1}{2}\sin\left(\frac{x}{4}\right) ).

Step2: Find the reciprocal of the sine function

The reciprocal of ( \sin(u) ) is ( \csc(u) ), where ( u=\frac{x}{4} ) in this case.

Step3: Replace ( \sin\left(\frac{x}{4}\right) ) with ( \csc\left(\frac{x}{4}\right) ) in the original function

Substituting the reciprocal function into the original equation, we get: ( y = -\frac{1}{2}\csc\left(\frac{x}{4}\right) )

Answer:

( y = -\frac{1}{2}\csc\left(\frac{x}{4}\right) )