1. 6-5 Translating Sine and Cosine

2. Phase Shift: A horizontal shift in trigonometric functions To phase shift, add/subtract c y= A sin (kθ + c) where the shift is −𝑐 𝑘 Positive C- shift left Negative C- shift right

3. Describe the phase shift in y=sin(θ+π)
Describe the phase shift in y=cos(2θ - 𝜋 2 )

4. 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 up
Negative h: shift down

5. y=A(sinkθ + C) + k Lets Review Period (length) Amplitude (height)
Vertical Shift
(up/down)
Phase Shift
(left/right)

6. 3) Given the function y=-2(cos4θ + 𝜋 4 ) -5, find the…
Amplitude
Period
Phase Shift
Vertical Shift
Midline equation

7. To Graph by hand… Find the vertical shift, and graph the midline.
Find the amplitude. Sketch out highest/lowest point
Find the period, then graph the sin/cos function
Shift the function over for the appropriate phase shift

8. 4) Find the amplitude, period, phase shift, and midline of the function, then graph y= 4(cos 𝜃 2 +π) -6

9. Find the amplitude, period, phase shift, and midline of the function, then graph
y=-2(cos𝜃/3+4π) +1

10. Compound Function: a graph that consists of sums or products of both trigonometric and linear functions Ex) y= sinx * cosx y= x + sinx To graph: Graph both functions on the same axis. Then, add/multiply the corresponding coordinates to find the new y value.

11. Graph y = x + cosx x
Cos(x)
X + cos(x)
π/2 π 2π
5𝜋 2