Trigonometric Function Translations

Equation to transform cos

a(cosθ - h) + k

Equation to transform sin

a(sinθ -h) + k

Equation to transform tan

a(tanθ - h) + k

a stands for

amplitude, 1/2 (maximum value - minimum value)

h is a called a

phase shift

If h<0

shift h units to the left

If h>0

shift h units to the right

iIf k<0

shift k units down

If k>0

shift k units up

if a <0

the graph will have lower peaks and valleys If a is 1/2, the maximum value is 1/2, the minimum value is -1/2

if a>0 then

the graph will have steeper peaks and valleys If a is 2, the maximum value is 2, the minimum value is -2