4.2 Graphing Sine and Cosine Period

4.1 Review Parent graphs f(x) = sin(x) and g(x) = cos(x) For y = a*sin(bx - c) + d and y = a*cos(bx - c) + d, the sinusoidal axis is y = d and the amplitude is |a|. To graph: 1)Graph SA 2)Find period 2π/b 3)Mark off each increment on x- axis period/4 4)Plot the following points (opposite if a is neg, max = d + |a|, min = d – |a|, start on y-axis and go 1 increment at a time): Sin – SA, max, SA, min Cos – Max, SA, min, SA

Period A function with period P will repeat on intervals of length P, and these intervals are referred to as periods. Typically, sine and cosine take 2π to repeat. The period can be altered. With a graph, you can determine period by finding the horizontal distance between consecutive maximums or minimums.

What are some things that are periodic? Ex: Average daily temperature

Graphing Calculator Investigation Graph each of the following and determine the period of the function. Then, try to figure out how to determine period from just the equation. Y = sin(2x)y = cos(4x) - 2 Y = 2sin(x/2) + 1y = -3cos(πx/12) Y =-4sin(πx – 1)y = 2cos(πx/2 + 2)

Even and Odd b must always be positive. We can use even and odd properties to make it + if it is not. Sin is _________Cos is _________ Use even and odd properties to make b +: Sin(-2x) Cos(-π/2) Cos(-3x – π) Sin(5 - πx/4)

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

Homework Find the amplitude, period, increment, S.A., domain and range and graph each function: Y = 2cos4x – 1 Y = -2sin(x/4) Y = -3cos2x +3 Y = 4sin3x Y = -cos(x/2) Y = 2sin4x - 2