Trig Functions

a=

amplitude/vertical stretch, distance between min and max, min-max/2

b=

frequency, old period/new period (new period = the time it takes to complete one cycle/end angle minus the start angle)

c=

phase shift

d=

vertical translation, max+min/2

y=sinx

iMimi, 0 to 2pi, period length of 2 pi, looks like bowtie

y=cosx

MimiM, 0 to 2pi, period length of 2 pi, looks like uterus

y=cscx

APANA, 0 to 2pi, period length of 2 pi, looks like first a positive “u” on the right side then an upside down negative “u” on the left side, 3 asymptots

y=secx

APANA, (-pi/2) to (3pi/2), period length of 2 pi, looks like first a positive “u” on the right side then an upside down negative “u” on the left side, find phase shift based off middle number

y=tanx

ANIPA, (-pi/2) to (pi/2), period length of pi, looks like a quadratic, find phase shift based off middle point

y=cotx

APINA, 0 to pi, period length of pi, looks like a vertically reflected quadratic