4 6 graphs of other trigonometric functions
Download
Skip this Video
Download Presentation
4.6 Graphs of Other Trigonometric FUNctions

Loading in 2 Seconds...

play fullscreen
1 / 24

4.6 Graphs of Other Trigonometric FUNctions - PowerPoint PPT Presentation


  • 121 Views
  • Uploaded on

4.6 Graphs of Other Trigonometric FUNctions. How can I sketch the graphs of all of the cool quadratic FUNctions?. Graph of the tangent FUNction. The tangent FUNction is odd and periodic with period π .

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' 4.6 Graphs of Other Trigonometric FUNctions' - naoko


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.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
4 6 graphs of other trigonometric functions

4.6 Graphs of Other Trigonometric FUNctions

How can I sketch the graphs of all of the cool quadratic FUNctions?

graph of the tangent function
Graph of the tangent FUNction
  • The tangent FUNction is odd and periodic with period π.
  • As we saw in Section 2.6, FUNctions that are fractions can have vertical asymptotes where the denominator is zero and the numerator is not.
  • Therefore, since , the graph of will have vertical asymptotes at , where n is an integer.
let s graph y tan x
Let’s graph y = tan x.
  • The tangent graph is so much easier to work with then the sine graph or the cosine graph.
    • We know the asymptotes.
    • We know the x-intercepts.
y 2 tan 2x
y = 2 tan (2x)
  • Now, our period will be
  • Additionally, the graph will get larger twice as quickly.
  • The asymptotes will be at
  • The x-intercept will be (0,0)
slide7

The period is 2π.

  • The asymptotes are at ±π.
  • The x-intercept is (0,0).
graph of a cotangent function
Graph of a Cotangent FUNction
  • Like the tangent FUNction, the cotangent FUNction is
    • odd.
    • periodic.
    • has a period of π.
  • Unlike the tangent FUNction, the cotangent FUNction has
    • asymptotes at period πn.
y cot x
y = cot x
  • The asymptotes are at ±πn.
  • There is an x-intercept at
y 2 cot 2x
y = -2 cot (2x)
  • The period is
  • There is an x-intercept at
  • There is an asymptote at
graphs of the reciprocal functions
Graphs of the Reciprocal FUNctions
  • Just a reminder
    • the sine and cosecant FUNctions are reciprocal FUNctions
    • the cosine and secant FUNctions are reciprocal FUNctions
  • So….
    • where the sine FUNction is zero, the cosecant FUNction has a vertical asymptote
    • where the cosine FUNction is zero, the secant FUNction has a vertical asymptote
slide15

And…

    • where the sine FUNction has a relative minimum, the cosecant FUNction has a relative maximum
    • where the sine FUNction has a relative maximum, the cosecant FUNction has a relative minimum
    • the same is true for the cosine and secant FUNctions
  • Let’s graph y = csc x
now you try your own
Now, you try your own….
  • Just graph the FUNction as if it were a sine or cosine FUNction, then make the changes we have already made.
damped trigonometric graphs just for fun
Damped Trigonometric Graphs (Just for Fun!)
  • Some FUNctions, when multiplied by a sine or cosine FUNction, become damping factors.
  • We use the properties of both FUNctions to graph the new FUNction.
  • For more fun on damping FUNctions, please read p 339 in your textbook.
slide23

For a nifty summary of the trigonometric FUNctions, please check out page 340.

  • As a matter of fact, I would make sure I memorized all of the information on page 340.
writing about math
Writing About Math
  • Please turn to page 340 and complete the Writing About Math – Combining Trigonometric Functions.
  • You may work with your group.
  • This activity is due at the end of the class.
ad