1. Take out your homework from last night
Answers to the Even Problems:
Amplitude: 4
Period: 360
Phase Shift: right 60
Vertical Shift: down 1
Midline: y=-1
Amplitude: 1/2
Period: 2π
Phase Shift: right π/2
Vertical Shift: up 4
Midline: y=4
Amplitude: 5
Period: π
Phase Shift: right π
Vertical Shift: up 3
Midline: y=3
Amplitude: Undefined
Period: 180
Phase Shift: left 30
Vertical Shift: down 2
Midline: y=-2

2. Warm-Up
Identify the amplitude, period, phase shift, vertical shift, and midline for the following graphs: 1. 𝑦=3 cos 2 𝜃− 𝜋 𝑦=2 tan 1 2 𝜃+90 −2 3. 𝑦=2+ sin 1 2 𝜃
Amplitude: 3
Period: π
Phase Shift: right π/4
Vertical Shift: up 1
Midline: y=1
Amplitude: undefined
Period: 360
Phase Shift: left 90
Vertical Shift: down 2
Midline: y=-2
Amplitude: 1
Period: 720
Phase Shift: none
Vertical Shift: up 2
Midline: y=2

4. 12.8 Graphing Trig Functions with Translations
Steps for Graphing Trig Functions:
y= a sin b(θ-h)+k
Draw midline y=k.
Draw dashed lines a units above and below midline for the amplitude.
Graph the function using the period without phase shift (need b).
Translate the graph h units.

5. 13. Graph: 𝑦=3 cos 𝜃−𝜋 +4
-4π π π π
π π π π

6. 14. Use the same procedure to graph: 𝑦=2 cos 1 2 𝜃+ 𝜋 2 −2
-4π π π π
π π π π

8. Partner Relay Practice
Every set of partners needs a whiteboard, two markers, an eraser, and a piece of paper.
One partner will be the recorder writing solutions on paper.
The other partner will be the artist writing the solutions on the whiteboard.
Make sure the recorder is writing down what the artist does on the white board.
Start on the blank side of the whiteboard without the coordinate plane.

9. Graph 𝑦= 1 2 cos 𝜃 +3
Determine the amplitude, period, phase shift, vertical shift, and midline.
Draw the midline.
Draw dash marks for the amplitude.
Draw the curve without the phase shift using the period.

10. Graph 𝑦= 1 2 tan (𝜃− 𝜋 2 )
Determine the amplitude, period, phase shift, vertical shift, and midline.
Draw the midline.
Draw dash marks for the amplitude.
Draw the curve without the phase shift using the period.
Draw the final curve with the phase shift.

11. Graph 𝑦=2 sin 2 𝜃+ 𝜋 4 −3
Determine the amplitude, period, phase shift, vertical shift, and midline.
Draw the midline.
Draw dash marks for the amplitude.
Draw the curve without the phase shift using the period.
Draw the final curve with the phase shift.

12. Graph 𝑦=4 tan 𝜃+𝜋 −1
Determine the amplitude, period, phase shift, vertical shift, and midline.
Draw the midline.
Draw dash marks for the amplitude.
Draw the curve without the phase shift using the period.
Draw the final curve with the phase shift.

13. Graph 𝑦=3 sin 2 𝜃− 𝜋
Determine the amplitude, period, phase shift, vertical shift, and midline.
Draw the midline.
Draw dash marks for the amplitude.
Draw the curve without the phase shift using the period.
Draw the final curve with the phase shift.

14. Graph 𝑦=2 cos 3 𝜃+45 +2
Determine the amplitude, period, phase shift, vertical shift, and midline.
Draw the midline.
Draw dash marks for the amplitude.
Draw the curve without the phase shift using the period.
Draw the final curve with the phase shift.

15. Homework
12-8 Worksheet The axis are already drawn for you Do not change the scale for the x-values!