1 / 30

4.1.2: What Does the Unit Circle Tell Me?

4.1.2: What Does the Unit Circle Tell Me?.

toshi
Download Presentation

4.1.2: What Does the Unit Circle Tell Me?

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. 4.1.2: What Does the Unit Circle Tell Me? Today you will learn how sine and cosine can be viewed in terms of the unit circle; develop the Fundamental Pythagorean Identity; and use the unit circle, the Fundamental Pythagorean Identity, and right triangles to find the values of trigonometric functions.

  2. Homework 4.1.1

  3. Homework 4.1.1

  4. Homework 4.1.1

  5. Today

  6. 4-15: Together as a class

  7. 4-16 Definitions of sine and cosine for all angles

  8. Partner problems Complete 4-17 & 4-18 with your partner

  9. Class Discussion: Reference Angles

  10. Partner problems Complete 4-20 & 4-21 with your partner

  11. Partner problems Complete 4-22 & 4-23 with your partner

  12. 4.1.3: How Can I Build a Wave? Today you will generate the graphs of sine and cosine using the unit circle as well as find the domain, range, and intercepts for the sine and cosine graphs.

  13. Today . . .

  14. Graphing the Sine Function • Complete the table of values • Now plots your points!! 0 0 1 -1 0

  15. Graphing the Cosine Function • Complete the table of values • Now plots your points!! 1 0 -1 0 1

  16. Comparing the Sine and the Cosine Graph

  17. Domain and Range • The domain is the section of graph where the function exists from left to right. The domain is also thought of as the set of all possible inputs that make the function true. • The range is the section of the graph where the function exists from bottom to top. The range is also thought of as the set of all possible outputs that make the function true.

  18. Domain and Range For the non-transformed sine and cosine function: • The domain is ______________. (interval notation) • The range is ________________. (interval notation)

  19. Period and Amplitude • Graphically, the period is one “cycle” of the graph. That is… the horizontal distance the graph travels before it repeats the same pattern. • Amplitude is the height from the line of oscillation. Or I will call this the ‘center line.’ • NOT from highest point to lowest point!!!

  20. Period and Amplitude For the non-transformed sine and cosine functions: • The period is ____________. • The amplitude is ____________.

  21. Transformations Review Reflect over x-axis Left/ Right Vertical Stretch/ Shrink Up/Down Horizontal Stretch/ Shrink

  22. Looking Ahead • Tomorrow is the Chapter 3 Individual Test! • Thursdayyou will be working on both homework assignments in class (4.1.2 & 4.1.3). Please work together and help each other out. • Fridaywe will be transforming the basic sine and cosine graphs. If you have a solid grasp of what the basic sine and cosine graphs look like and what their basic characteristics are (maximum points, minimum points, where it crosses center line (crossings), period, amplitude, domain, range, etc.) the easier it will be to transform the graphs.

  23. assignment HW 4.1.2 4-24 to 4-31 (pg. 187) See yutmrrw!

  24. Assignment HW 4.1.3 4-38 to 4-46 (pg. 192)

More Related