1 / 27

Graphing Variations of the Sine Function: Understanding Amplitude and Period

This lesson explores how to graph variations of the sine function, focusing on properties such as amplitude and period. Using the graph of ( y = sin x ) on the interval ( 0 < x < 2pi ), we demonstrate how to identify key points by dividing the period into four equal parts. The amplitude affects the height of the graph, as seen when comparing ( y = sin x ) and ( y = 2sin x ). Learners will also explore how the factor ( B ) impacts graph stretching and compression. Practical examples enhance understanding of sine function transformations.

stephen-hunter
Télécharger la présentation

Graphing Variations of the Sine Function: Understanding Amplitude and Period

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Trigonometry

  2. Aim# 4-5A: How do we graph variations of sine function? • Here are some values of (x, y) on the graph of y = sin x on the interval 0 < x < 2π.

  3. This is the graph of y = sin x. • Remember that one complete cycle for the sine function is 2π

  4. This is a more complete graph of y=sin x. Why? • Remember the sine is an ODD function so it has symmetry along the origin.

  5. The graph of y= sin x illustrates the following properties:

  6. Graphing variations of Y = Sinx • To graph a variation of y= sin x remember:

  7. Note when the function reaches its max. and min. points and other key points.

  8. In graphing variation of the sine function, key points can be found by dividing the period into 4 equal parts. • The y-coordinate can be found by evaluating the x-value.

  9. Y = A sinx Ex: y =2 sinx A = 2 We can graph this by multiplying the y-values by 2. A stands for the Amplitude of the function. How do you think the graph of y= sin x will change?

  10. Y= 2 sin x The graph stretched. The range is now [-2,2] instead of [-1,1]. .

  11. Graphing Variations of y= sin x.

  12. Example 1: Graphing a Variation of y= sinx

  13. Example 2:

  14. Graph:

  15. Amplitudes and Periods • If B >1 the graph will shrink by a factor of 1/ B • If 0<B<1 the graph will STRETCH by a factor of 1/B

  16. Example 3:

  17. Now let’s find the 5 key points.

  18. The Graph of y=3 sin 2x

  19. Check for Understanding: 1.Determine the amplitude of y= 3 sinx. Then graph y= sin x and y= 3 sin x for 0< x <2π. 2. Determine the amplitude of y= -1/2 sinx. Then graph y= sin x and y= -1/2 sin x for - π< x < 3π. 3.Determine the amplitude of y= 2 sin 1/ 2x. Then graph for 0< x <8π.

  20. Summary: Answer in complete sentences. • How does the Amplitude affect the graph of y= sin x? • How do you find the period of the sine function? • How does B affect the graph?

More Related