Graphing Trig Functions Name ________________________________________ Part I: Find the period and Amplitude of each equation: Match Each of the Functions to the graphs below. Then state the Amplitude and Period of each function. Example 1: Sketch the graph of for where = 5, = 2, and = 3. a b c Discuss the intercepts and the maximum and minimum points. As the value of approaches zero, explain the change in value of . a As the value of increases, explain the change to the corresponding graph. b Example 2: Consider the functions and . it’s parent function Which function has the larger amplitude? Write a function that has a smaller amplitude then either or . Write a function that has a longer period then either or . If , describe the transformation from . Example 3: A supporting post on a pier shows the height of the water as 5.4 feet at low tide (2AM) and a height of 11.8 feet at the next high tide, 6.2 hours later. Write an equation describing the depth of the water at this location hours after midnight. t What will be the depth of the water at this support at 4 AM? Example 4: The height of a seat on a Ferris wheel with a diameter of 14 meters, seconds after it begins to turn at 3 rpm, can be computed using this sinusoidal model, . t Graph the function. When will the height of the seat be a minimum? A maximum? What are these heights? If the wheel is replaced with one with a larger diameter, 16 feet, how would the parameters in the
Graphing Trig Functions Name ________________________________________ Part I: Find the period and Amplitude of each equation: Match Each of the Functions to the graphs below. Then state the Amplitude and Period of each function. Example 1: Sketch the graph of for where a = 5, b = 2, and c = 3. Discuss the intercepts and the maximum and minimum points. As the value of a approaches zero, explain the change in value of . As the value of b increases, explain the change to the corresponding graph. Example 2: Consider the functions and it’s parent function . Which function has the larger amplitude? Write a function that has a smaller amplitude then either or . Write a function that has a longer period then either or . If , describe the transformation from . Example 3: A supporting post on a pier shows the height of the water as 5.4 feet at low tide (2AM) and a height of 11.8 feet at the next high tide, 6.2 hours later. Write an equation describing the depth of the water at this location t hours after midnight. What will be the depth of the water at this support at 4 AM? Example 4: The height of a seat on a Ferris wheel with a diameter of 14 meters, t seconds after it begins to turn at 3 rpm, can be computed using this sinusoidal model, . Graph the function. When will the height of the seat be a minimum? A maximum? What are these heights? If the wheel is replaced with one with a larger diameter, 16 feet, how would the parameters in the
hw_graph_trig_packet.docx