6-5 translating sine and cosine
DESCRIPTION
6-5 Translating Sine and Cosine. Phase Shift : A horizontal shift in trigonometric functions To phase shift, add/subtract c y= A sin (k θ + c) where the shift is Positive C- shift left Negative C- shift right. - PowerPoint PPT PresentationTRANSCRIPT
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 ______________