Chapter 4: Circular Functions Lesson 7: Scale-Change Images to Trig Functions Mrs. Parziale

Parent Sine or Cosine Function: General form of Sine or Cosine Function:

Example 1: Using your TI83, Graph and Compare the following functions. How do these two graphs compare? – What are their maximum points? – What are their minimum points? – What relationship do you see with the equation? – What is the amplitude?

What’s the Amplitude? What is the amplitude of the following equations? a) b) c)

Example 2: Using your TI83, Graph and Compare the following functions. Describe how the two graph are different. – What is the value of the maximum? – What is the value of the minimum? – How many cycles of the sine curve are there on each graph from 0 to 2  ? – What is the Period?

How Many Cycles? How many cycles of the sine curve are on the graphs for the equations below? a) b) c)

Example 3: Identify the amplitude and period for the following sine functions. amplitude: ____ period: _______ amplitude: ____ period: _______

Example 3, cont.: Identify the amplitude and period for the following sine functions. amplitude: ____ period: _______

Graphing Sine and Cosine Functions: To graph the sine and cosine functions, you need five key points which include the x- and y-intercepts and the maximum and minimum points. Take the following steps when graphing the sine and cosine functions. Step 1: Find the amplitude and period of the function. Step 2: Divide the section of the graph into four equal parts. Step 3: Find the intercept points. Step 4: Find the max and min points. Step 5: Graph the five points and draw a smooth curve through them.

Example 4: Graph Amplitude = ________ Period = __________ x-intercepts = ______, _____, y-intercept = ______ max = _________ min = _________

Example 5: Graph Amplitude = ________ Period = __________ x-intercepts = ______, _____, y-intercept = ______ max = _________ min = _________

Example 6: Graph Amplitude = ________ Period = __________ x-intercepts = ______, _____, y-intercept = ______ max = _________ min = _________

Example 7: Graph Amplitude = ________ Period = __________ x-intercepts = ______, _____, y-intercept = ______ max = _________ min = _________

Graphing the Tangent Function The parent tangent function has a period of . When graphing the tangent function, you will need to know the x-intercept, vertical asymptotes, the halfway points, and the period. Period = ___________ Vertical asymptotes are defined at odd multiples of ______________

Example 8: Graph. Period = _______ x-intercept = _______ Vertical Asymptotes = ________ Halfway points = ___, ___

Closure Given the equation What is the amplitude? Explain how an amplitude of ½ affects the graph compared to the parent function? How many cycles appear within 2 π? What is the period of the curve? How does a period of affect the graph?