- By
**vic** - Follow User

- 140 Views
- Uploaded on

Download Presentation
## PowerPoint Slideshow about 'Section 4.6' - vic

**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

### Section 4.6

Graphs of Other Trigonometric Functions

Overview

- In this section we examine the graphs of the other four trigonometric functions.
- After looking at the basic, untransformed graphs we will examine transformations of tangent, cotangent, secant, and cosecant.
- Again, extensive practice at drawing these graphs using graph paper is strongly recommended.

Tangent and Cotangent

- Three key elements of tangent and cotangent:
- For which angles are tangent and cotangent equal to 0? These will be x-intercepts for your graph.
- For which angles are tangent and cotangent undefined? These will be locations for vertical asymptotes.
- For which angles are tangent and cotangent equal to 1 or -1? These will help to determine the behavior of the graph between the asymptotes.

Transformations

|A| = amplitude (affects the places where tangent or cotangent is equal to 1 or -1)

π/B = period (distance between asymptotes). The asymptotes will keep their same relative position

C/B = phase (horizontal) shift. Left if (+), right if (-)

Secant and Cosecant

- The graphs of secant and cosecant are derived from the graphs of cosine and sine, respectively:
- Where sine and cosine are 0, cosecant and secant are undefined (location of vertical asymptotes).
- Where sine and cosine are 1, cosecant and secant are also 1.
- Where sine and cosine are -1, cosecant and secant are also -1.

Transformations

- To graph a transformation of cosecant or secant, graph the transformation of sine or cosine, respectively, then use the reciprocal strategy previously discussed:

|A| = amplitude (affects the places where secant or cosecant is equal to 1 or -1)

2π/B = period (distance between asymptotes)

C/B = phase (horizontal) shift, left if (+), right if (-)

Download Presentation

Connecting to Server..