Graph y=2csc(x)

Problem

y=2*csc(x)

Solution

1. Identify the parent function and its properties. The function y=csc(x) is the reciprocal of sin(x) meaning y=1/sin(x)

2. Determine the vertical asymptotes. Since csc(x) is undefined when sin(x)=0 vertical asymptotes occur at x=n*π for any integer n

3. Apply the vertical stretch. The coefficient 2 in y=2*csc(x) stretches the graph vertically by a factor of 2

4. Locate the relative extrema. The local minima of the parent function occur at x=π/2+2*n*π with a value of 1 for y=2*csc(x) these points move to (π/2,2)

5. Locate the relative maxima. The local maxima of the parent function occur at x=(3*π)/2+2*n*π with a value of −1 for y=2*csc(x) these points move to ((3*π)/2,−2)

6. Sketch the curves. Draw U-shaped branches between the asymptotes, starting from the local extrema and approaching the vertical asymptotes.

Final Answer

y=2*csc(x)

Want more problems? Check here!