November 29, 2012 Period and Amplitude of the Sine and Cosine Functions Warm-up: Finish Sine and Cosine Function Activity (15 minutes) HW 4.5: Pg #1-6, 35-43

sin 0 π/2 Π 3π/2 2π2π 1 π/2π3π/22π2π Lesson 4.5 The Sine Function

cos 0 π/2 Π 3π/2 2π2π The Cosine Function 1 π/2π3π/22π2π

Sketch the sine and cosine curve from -2π to 2π Always use the intercepts, maximum, and minimum points to sketch sine or cosine curve. y = sin x y = cos x θ θ

Finding Amplitude of Sine and Cosine Graphs The amplitude of the graphs is how high and low your graph goes from the x-axis. *The range of the function. What is the amplitude for y = sinx and y = cosx? |a| is the magnitude or the amplitude of the graph. y = a sinθ ory = a cosθ Example: What is the amplitude of y = 3 cosx ?

Graphing with different amplitudes Graph y = 2 sinx 1 π/2π3π/22π2π st : graph the zeroes 2 nd : graph max and min

Sketch a graph of each, then identify the intercepts, max, and min. π/2π3π/22π2ππ/2π3π/22π2π Vertical Shrink Vertical Stretch

Finding the Period of Sine and Cosine Graphs The period of the sine and cosine curves is the angle at which the curve repeats its pattern. The period changes if you multiply the angle by some factor, b: y = sin(b)y = cos(b) Period of sine or cosine = What is the period of y = cos(2x)?

Graph y = cos(2x), include 2 full periods 1)Identify the period and amplitude. 2) Divide the period into four parts (these will be our zeros, max and mins since sine and cosine always follow the same pattern!) 3) Use your answer from 2 to scale your x-axis Horizontal Shrink

Graph, include 2 full periods Horizontal Stretch 1)Identify the period and amplitude. 2) Divide the period into four parts (these will be our zeros, max and mins since sine and cosine always follow the same pattern!) 3) Use your answer from 2 to scale your x-axis

Start HW 4.5 #1 and #37, 39 1.Find the period and amplitude: y = 3 sin 2x, then sketch 37.Sketch the graph 39. Sketch the graph