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How do you graph #y=3csc(x-pi/2)-2#?

1 Answer
Jun 7, 2018

Answer:

As below

Explanation:

Standard form of cosecant function is #color(crimson)(y = A csc (Bx - C) + D#

Given function is #y = 3 csc (x - pi/2) - 2#

#A = 3, B = 1, C = pi/2, D = -2#

#color(maroon)("Amplitude " = |A| = "None for cosecant function"#

#color(maroon)("Period " = (2pi)/|B| = 2pi#

#color(maroon)("Phase Shift " = -C / B = pi/2), pi/2 # " to the right"

#color(maroon)("Vertical Shift " = D = -2#

graph{3 csc (x - (pi/2)) - 2 [-10, 10, -5, 5]}