6-5 Translating Sine and Cosine

Phase Shift: A horizontal shift in trigonometric functions

To phase shift, add/subtract cy= A sin (kθ + c) where the shift is

Positive C- shift leftNegative C- shift right

(hint: when graphing with a phase shift, trying labeling in units same as phase shift)

1) Describe the phase shift in y=sin(θ+π)

2) Describe the phase shift in y=cos(2θ - )

Midline: a horizontal axis that is used as the reference line about which the graph of a periodic function oscillates (middle of the graph)

Vertical Shift: add/subtract h to function such as:y= A sin(kθ + c) + h

Positive h : shift upNegative h: shift down

Lets Review

y=A(sinkθ + C) + h

Amplitude(height)

Period(length) Phase Shift

(left/right)Vertical Shift(up/down)

3) Given the function y=-2(cos4θ + ) -5, find the…

a) Amplitude

b) Period

c) Phase Shift

d) Vertical Shift

e) Midline equation

3) Given the function y=4 (cos2θ + ) +1, find the…

a) Amplitude

b) Period

c) Phase Shift

d) Vertical Shift

e) Midline equation

 Given the graph, fill in the blanks and write an equation to model the function:

period _______ k=_______

maximum ______________   minimum ______________

amplitude ______________

vertical slide ____________

phase shift (sine) _________c=

sine equation ______________