1 Consider the following trigonometric function A Determine

1: Consider the following trigonometric function

A: Determine the Phase Shift.

B: Determine the Period.

C: What would be the DOMAIN and RANGE of the function?

D: Make a sketch of the graph of the function below (label axes properly)

Solution

Use the form y=acsc(bxc)+d

where, a= amplitude, period=2pi/b, phase shift=c/b, and d= vertical shift.

given, y=-csc(2x-pi)+3=csc(2x)+3

(A) Phase shift=0/b=0

(B)period=2pi/b=2pi/2=pi

(C)Domain is,(n+1)pi/2<x<(n+2)pi/2 where n is integer

Range:- y<=2   or, y>=4

(D)so plot is