1. Warm-up
Y = -4cos(x/2) + 1 Graph and find the amplitude, period, increment, min, max, domain, range

2. 4.3 Graphing Sine and Cosine
Phase Shifts

3. Phase Shift Investigation
Usually sine and cosine start their patterns at x=0. We can change that by shifting them horizontally. Graph each of the following and look for a way to find the phase shift given the equation y = a*sin(bx-c) + d. Y = sin(x - 𝜋 4 ) y = -4sin(3x + π) + 2 Y = 2sin(x + 𝜋 8 ) y = -3sin(2x + 3𝜋 2 )

4. How do you find a phase shift?
Given y = a*cos(bx – c) + d

5. Let’s discuss these words…
Period, increment, phase shift, sinusoidal axis, amplitude, maximum, minimum, domain, range.

6. Guided Practice
Find the amplitude, period, increment, S.A., starting point, domain and range and graph each function:
Y = cos(x - 𝜋 4 )
Y = 3sin(x + 𝜋) -1
Y = -4cos(x – 2𝜋)
Y = 4sin(2x+ 𝜋 3 )
Y = cos(x/2 - 𝜋 3 ) - 3
Y = -4sin(3x + 𝜋 4 ) +6

7. Homework
Find the amplitude, period, increment, S.A., starting point, domain and range and graph each function:
Y = cos(x - 𝜋 2 )
Y = sin(x + 𝜋 3 ) -1
Y = -3cos(2x + 𝜋)
Y = 2sin(2x - 𝜋 2 )
Y = cos(x/2 + 𝜋 3 ) + 1
Y = -sin(3x + 𝜋 2 ) +2