Objectives:- Interpret phase shifts and vertical translations- Graph trig graphs with translations- Write equations to describe translations

Graph one period.

b. 𝑦𝑦 = sin(𝑥𝑥 + 𝜋𝜋)

Extra Practice

Sometimes it's hard to know how to do phase shifts. Here is another way to find your 5 main x-values to graph:

Set whatever is inside the trig function equal to the five x-values of and solve for x.

Solving these 5 short equations gives us 5 new x-valuesto graph. This is especially helpful when you have more than one transformation.

Once you have the x-values, the y-values are obtained from knowing the vertical shift & amplitude.

Graph one period.

Change the graphs to:a) 𝑦𝑦 = cos 𝑥𝑥 − 𝜋𝜋

2+ 5 b)𝑦𝑦 = 𝑐𝑐𝑐𝑐𝑐𝑐 𝑥𝑥 + 2𝜋𝜋 − 3

Graph one period.

Change to:a) 𝑦𝑦 = −3 sin 𝑥𝑥 − 𝜋𝜋

3+ 1 b) 𝑦𝑦 = 2𝑐𝑐𝑐𝑐𝑐𝑐 𝑥𝑥 + 𝜋𝜋 − 3

Graphing in the Calculator

a)𝑦𝑦 = 𝑐𝑐𝑠𝑠𝑠𝑠𝑥𝑥 + 2𝑥𝑥

b)𝑦𝑦 = 𝑐𝑐𝑐𝑐𝑐𝑐𝑥𝑥 + 𝑥𝑥

Assignment:

Section 6.7: problems 1 – 6, 9, 10, 12 – 14, 17 – 18, 25, 27, 29

On all graphs, list the period, amplitude, and graph at least one period.