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Module 4: Quick Reference
Graphs of Trig Functions
y = A sin(Bx − C) + D / y = A cos(Bx − C) + D
Amplitude = |A| Period = 2π/|B| Phase Shift = C/B Midline = D
Range = [D − |A|, D + |A|]
All Six Functions at a Glance
Function
Period
Range
Asymptotes
sin, cos
2π/|B|
[D−|A|, D+|A|]
None
tan, cot
π/|B|
(−∞, ∞)
Yes
sec, csc
2π/|B|
(−∞,−|A|]∪[|A|,∞)
Yes
Sine Key Points
(0,0) (π/2,1) (π,0) (3π/2,−1) (2π,0)
Cosine Key Points
(0,1) (π/2,0) (π,−1) (3π/2,0) (2π,1)
tan/cot asymptotes: where cos/sin = 0 | sec/csc: graph cos/sin first as guide