Graph y=3csc(x)

Problem

y=3*csc(x)

Solution

1. Identify the parent function and its properties. The function y=csc(x) is the reciprocal of y=sin(x) It has vertical asymptotes where sin(x)=0 which occur at x=n*π for any integer n

2. Determine the amplitude transformation. The coefficient 3 in y=3*csc(x) acts as a vertical stretch. While cosecant does not have an amplitude, the relative "peaks" and "valleys" of the curves will be shifted from 1 and −1 to 3 and −3

3. Locate the vertical asymptotes. Since the argument x is not modified, the asymptotes remain at x=…,−π,0,π,2*π,…

4. Find key points for one period. In the interval (0,2*π) the local minimum occurs at x=π/2 where y=3*csc(π/2)=3*(1)=3 The local maximum occurs at x=(3*π)/2 where y=3*csc((3*π)/2)=3*(−1)=−3

5. Sketch the curves. Draw the U-shaped branches between the asymptotes. One branch opens upward from the point (π/2,3) and another branch opens downward from the point ((3*π)/2,−3)

Final Answer

y=3*csc(x)

Want more problems? Check here!