6.5 Trigonometric Graphs

TRIGONOMETRIC GRAPHS

Graphing      :

Graphing      :

Graphing      :

• 'a' leads to vertical stretching. Vertical stretching will cause a change in amplitude.
• 'b' leads to horizontal compressing. Horizontal compressing will change the period.
• 'c' leads to shifting left or right. This left or right shifting is called a phase shift.
• 'd' leads to shifting up or down. This up or down shift is called a midline shift because it will affect the midline.

VERTICAL STRETCHING

 compared to 

AMPLITUDE/PERIOD

HORIZONTAL COMPRESSING

 compared to

L/R SHIFT (PHASE SHIFT)

 compared to              compared to 

The graph on the left is showing a left phase shift. The graph on the right shows a right phase shift.

U/D SHIFT (MIDLINE SHIFT)

This graph shows an upward midline shift.

This graph shows a downward midline shift.

MIDLINE

This graph shows 

 & in the thinner and wavy lining and their midline's in a thick line through the middle of each.

And that's about it, other than The Nonagon Song, of course.

Alex Hackert

6.2 Part 2 Identities

Identity: An equation which is true regardless of what values are substituted for any variables.

Identities apply to basic algebra as well as trigonometry, and especially to what we are learning.  Identities apply to sin, cos, and tan.  Because they each have a reciprocal we have learned about( csc, sec, and cot), its quite simple!  

These are reciprocal identities.  There are also Quotient Identities.  These are derived from the 3 basic trigonometric functions, using substitution based on their definitions: 

 and

Finally, in class Mr. Wilhelm helped us derive the 1st of 3 Pythagorean Identities, using the Pythagorean Theorem, and using substitution by definitions: 

Becomes...

To solve an identity, you must change and work with one side without altering the other.  As Mr. Wilhelm told us, it is best to work with the crazy messy side and try to work towards the nice clean one.  Lots of substituting!  

Soo thats basically it i think, except for :

http://www.youtube.com/watch?v=3nG1ckY7thw

Please Mr. Wilhelm, I've never seen it and I think to fully enjoy it we need to be all together in class as to create the right atmosphere.   :)

Good luck!

~Kendall

6.3 Graphs, Periods, and Even and Odd Functions

Why hello there! This is Nonny the Nonagon stopping by to help everyone with section 6.3. His good friend, Sergei the Circle has decided to come with him to help. Sergei is really good with explaining the graph of sin.


Now, Mr. Wilhelm told us how to look at a graph of sin. Although he had a fancy website, here's a picture showing how a point on a circle coincide with the sin of a point.  (This was Sergei's favorite example)

When you keep going around a circle to show the graph on sin, that wave, formally called a period, will keep repeating. A period is the smallest part of the wavelength on the graph before it repeats. 

Mr. Wilhelm also told us these two equations which go along with the graph below when:

                                                                                                                              

1)                         2) 

Basically, he's just showing us how the two angles are both solutions to the equation, although they are: in completely different quadrants and two different standard position angle measures.



Flashback to Honors Algebra 2 A, we went over functions today in class. Though we were a little rusty on them, we ended up figuring out how this section relates back. But before we get into it, lets review what even and odd functions are.

                                                                   
                                                   

Now, is there any difference between those functions and these?

   
The answer to that would be a no. All we did is change the x to a theta so we can use these equations for circles. But which trigonometric function goes with which? Good question.

Just remember than when you have the two functions below, your answer will always be an odd function.

That's about it for my part of the lesson, so until next time, Bye!

                                                                 

http://www.youtube.com/watch?v=x5ohtlewREI
http://www.youtube.com/watch?v=3nG1ckY7thw

-Kristy Griswold