40S Applied Math Mr. Knight – Killarney School Slide 1 Unit: Sinusoids Lesson: SIN-L4 Analyzing Sinusoidal Graphs Analyzing Sinusoidal Graphs Learning Outcome B-4 SIN-L4 Objectives: To determine the sinusoidal equation from a graph, or from data.

40S Applied Math Mr. Knight – Killarney School Slide 2 Unit: Sinusoids Lesson: SIN-L4 Analyzing Sinusoidal Graphs The parameters a, b, c, and d determine the shape and location of the graph of a sinusoidal function. 'a' determines the amplitude 'b' determines the period 'c' determines the horizontal shift 'd' determines the vertical shift You need to be very familiar with the graph of the basic sinusoidal function: Intro – Sinusoidal Function Review

40S Applied Math Mr. Knight – Killarney School Slide 3 Unit: Sinusoids Lesson: SIN-L4 Analyzing Sinusoidal Graphs You need to keep in mind that the graph of the basic sinusoidal function always: passes through the origin on its way to the maximum at x =  /2 the period is 2  the median line or axis is the x-axis When analyzing the graph of a sinusoidal function, you should first determine the values of the parameters, then write the equation in the form: y = a sin b(x + c) + d Intro – Sinusoidal Function Review

40S Applied Math Mr. Knight – Killarney School Slide 4 Unit: Sinusoids Lesson: SIN-L4 Analyzing Sinusoidal Graphs Write the equation in the form y = a sin b(x + c) + d for the graph shown below. Example 1

40S Applied Math Mr. Knight – Killarney School Slide 5 Unit: Sinusoids Lesson: SIN-L4 Analyzing Sinusoidal Graphs Write the equation in the form y = a sin b(x + c) + d for the graph shown below. Therefore, the equation of the graph is: y = 2 sin 1(x - 0) + 1, or y = 2 sin x + 1 Example 1

40S Applied Math Mr. Knight – Killarney School Slide 6 Unit: Sinusoids Lesson: SIN-L4 Analyzing Sinusoidal Graphs Write the equation in the form y = a sin b(x + c) + d for the graph shown below. Example 2

40S Applied Math Mr. Knight – Killarney School Slide 7 Unit: Sinusoids Lesson: SIN-L4 Analyzing Sinusoidal Graphs Write the equation in the form y = a sin b(x + c) + d for the graph shown below. Therefore, the equation of the graph is: Example 2

40S Applied Math Mr. Knight – Killarney School Slide 8 Unit: Sinusoids Lesson: SIN-L4 Analyzing Sinusoidal Graphs Write the equation in the form y = a sin b(x + c) + d for the graph shown below. Example 3

40S Applied Math Mr. Knight – Killarney School Slide 9 Unit: Sinusoids Lesson: SIN-L4 Analyzing Sinusoidal Graphs Write the equation in the form y = a sin b(x + c) + d for the graph shown below. Therefore, the equation of the graph is: y = 3 sin 2x + 0, or y = 3 sin 2x Example 3

40S Applied Math Mr. Knight – Killarney School Slide 10 Unit: Sinusoids Lesson: SIN-L4 Analyzing Sinusoidal Graphs Write the equation in the form y = a sin b(x + c) + d for the graph shown below. Example 4

40S Applied Math Mr. Knight – Killarney School Slide 11 Unit: Sinusoids Lesson: SIN-L4 Analyzing Sinusoidal Graphs Write the equation in the form y = a sin b(x + c) + d for the graph shown below. Therefore, the equation of the graph is: Example 4

40S Applied Math Mr. Knight – Killarney School Slide 12 Unit: Sinusoids Lesson: SIN-L4 Analyzing Sinusoidal Graphs Write the equation in the form y = a sin b(x + c) + d for the graph shown below. Example 5

40S Applied Math Mr. Knight – Killarney School Slide 13 Unit: Sinusoids Lesson: SIN-L4 Analyzing Sinusoidal Graphs Write the equation in the form y = a sin b(x + c) + d for the graph shown below. Example 5

40S Applied Math Mr. Knight – Killarney School Slide 14 Unit: Sinusoids Lesson: SIN-L4 Analyzing Sinusoidal Graphs Write the equation in the form y = a sin b(x + c) + d for the graph shown below. Example 6

40S Applied Math Mr. Knight – Killarney School Slide 15 Unit: Sinusoids Lesson: SIN-L4 Analyzing Sinusoidal Graphs Write the equation in the form y = a sin b(x + c) + d for the graph shown below. Example 6