Trigonometric Functions with Four Parameters

function

sin

cos

tan

sec

csc

cot

a

π

4

b

0.5

c

4.3

d

1.5

show equation with

values

symbols

show one period

This Demonstration plots the graph of

y-b

d

=f

x-a

c

for various trig functions

f

. Notice how changing the parameters maintains the overall shape of the graph, but stretches, squishes, or moves it. Can you explain why each parameter changes the graph the way it does? Are there relationships between the way parameter changes affect the graph and the location where they appear in the equation?