Find cosecant graph period, phase shift, and midline
Result
Cosecant Graph Features
Step-by-Step Derivation
Cosecant Graph Formula
y = A csc(Bx + C) + D
A cosecant graph is the reciprocal of a sine graph. It forms repeated branches separated by vertical asymptotes, so graph features focus on stretch and shifts.
⚠B must not be zero. Cosecant has no amplitude because its graph is unbounded.
How Cosecant Graph Analysis Works
The period follows the sine base period, while A controls vertical stretch, C shifts the graph horizontally, and D shifts the midline.
No Amplitude
Cosecant is unbounded.
Period
Period is 2π/|B|.
Phase Shift
Phase shift is -C/B.
Midline
Midline is y=D.
💡 Example: For y=-2csc(4x+8)-1, stretch=2, period=π/2, phase shift=-2, midline y=-1.
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