Components of Trig Graphs

amplitude

| a | or (max - min)/2

period (sin/cos/csc/sec)

2π/b

period (tan/cot)

π/b

axis of wave

y = d or (max + min)/2

phase shift

horizontal displacement ( -c units)

vertical shift

d units (d>0 up, d<0 down)

maximum

d + a (vertical shift + amplitude)

minimum

d - a (vertical shift - amplitude)

cotangent asymptotes

bx + c = “old” asymptote

secant/cosecant asymptote

x = 1st asymptote + ½ period n

writing asymptote in domain (tan/cot)

x ∈ R | 1st asymptote + period n, n ∈ I

writing asymptote in domain (sin/cos/csc/sec)

x ∈ R | 1st asymptote + ½ period n, n ∈ I