Take out your homework from last night Answers to the Even Problems: 26. 30. 28. 32. 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

Warm-Up Identify the amplitude, period, phase shift, vertical shift, and midline for the following graphs: 1. 𝑦=3 cos 2 𝜃− 𝜋 4 +1 2. 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

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.

13. Graph: 𝑦=3 cos 2 3 𝜃−𝜋 +4 -4π -3π -2π -π π 2π 3π 4π

14. Use the same procedure to graph: 𝑦=2 cos 1 2 𝜃+ 𝜋 2 −2 -4π -3π -2π -π π 2π 3π 4π

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.

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.

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.

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.

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.

Graph 𝑦=3 sin 2 𝜃− 𝜋 2 +4 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.

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.

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