1 / 12

Understanding Sine and Cosine: Periodic Functions and Their Graphs

This section explores sine and cosine as periodic functions defined through the unit circle. When an angle's terminal side intersects the unit circle at point P(x,y), we establish that x = cos(θ) and y = sin(θ). The graph of y = sin(θ) is analyzed both in degrees and radians to illustrate periodicity, cycles, and their behavior. Additionally, we relate these concepts to real-life applications such as musical tones produced by vibrating strings, linking frequency and period with graphing exercises. Includes practice problems for reinforcement.

linus-ware
Télécharger la présentation

Understanding Sine and Cosine: Periodic Functions and Their Graphs

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. section 13.6b Sine & Cosine Periodic Functions

  2. Def: If the terminal side of an angle is in standard position and intersects the unit circle at P(x,y) then x = cos Ɵ and y = sin Ɵ Trig functions defined using the unit circle are called circular functions.

  3. I. Graph y = sin Ɵ using the unit circle Periodic Function Circular Function 1 0   -1 0o 90o 180o 270o 360o Sin 

  4. Graph of the Sine (Degree Mode) The cycle starts to repeat ? The cycle starts ?

  5. Graph of the Sine (Radian Mode) The cycle starts ? The cycle starts to repeat ?

  6. Graph of the Cosine (Radian Mode) The cycle starts ? The cycle starts to repeat ?

  7. 5. Find the period of the Periodic Function The cycle ends ? The cycle starts ?

  8. 6. Find the period for each Periodic Function

  9. Find the exact value of each 7.) 8.)

  10. 9.) When a string is plucked on a harp, it is displaced from a fixed point to the middle of the string and vibrates back and forth, producing a musical tone. The exact tone depends on the frequency, or number of cycles per second, the string vibrates. Middle C has a frequency of 278 cycles per second or 278 hertz.

  11. 9.) continued: Middle C has a frequency of 278 cycles per second or 278 hertz. • What is the period? • Graph the function: Time in seconds displacement

  12. Homework Page 808 Problems: #11-28 all

More Related