Graph y=-csc(x)

Problem

y=−csc(x)

Solution

1. Identify the parent function as y=csc(x) which is the reciprocal of the sine function, y=sin(x)

2. Determine the vertical asymptotes by finding where sin(x)=0 which occurs at x=n*π for any integer n

3. Apply the vertical reflection across the xaxis due to the negative sign in front of the cosecant function.

4. Locate the relative extrema: the local minima of y=csc(x) at (π/2+2*n*π,1) become local maxima at (π/2+2*n*π,−1) and the local maxima at ((3*π)/2+2*n*π,−1) become local minima at ((3*π)/2+2*n*π,1)

5. Sketch the curves between the asymptotes, ensuring the branches open downward from y=−1 and upward from y=1

Final Answer

y=−csc(x)

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