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Module 4 Study Guide: Graphs of Trig Functions

Trigonometry • Learn Without Walls

General Sinusoidal Form

y = A sin(Bx − C) + D   or   y = A cos(Bx − C) + D
ParameterMeaningFormula
|A|AmplitudeHeight from midline to peak
2π/|B|PeriodLength of one cycle
C/BPhase shiftHorizontal translation
DVertical shiftMidline y = D
Range = [D − |A|, D + |A|]

Tangent and Cotangent

Period of tan/cot = π/|B| (not 2π/|B|)
tan x: asymptotes at x = π/2 + nπ, increasing branches
cot x: asymptotes at x = nπ, decreasing branches

Secant and Cosecant

Graph sec by sketching cos first; graph csc by sketching sin first
sec x: asymptotes where cos = 0; range (−∞,−1]∪[1,∞); period 2π
csc x: asymptotes where sin = 0; range (−∞,−1]∪[1,∞); period 2π

Graphing Steps

  1. Find A, B, C, D
  2. Calculate amplitude, period, phase shift, vertical shift
  3. Draw midline y = D
  4. Mark one period starting at x = C/B
  5. Divide into 4 parts, plot 5 key points
  6. Connect smoothly and extend