2 3 trigonometric functions the unit circle approach
Download
Skip this Video
Download Presentation
2.3 Trigonometric Functions: The Unit Circle Approach

Loading in 2 Seconds...

play fullscreen
1 / 7

2.3 Trigonometric Functions: The Unit Circle Approach - PowerPoint PPT Presentation


  • 149 Views
  • Uploaded on

2.3 Trigonometric Functions: The Unit Circle Approach. Definition of Trigonometric Functions Calculator Evaluation Application Summary of Sign Properties. Trigonometric Functions. The Unit Circle .

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 ' 2.3 Trigonometric Functions: The Unit Circle Approach' - phil


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
2 3 trigonometric functions the unit circle approach
2.3 Trigonometric Functions: The Unit Circle Approach
  • Definition of Trigonometric Functions
  • Calculator Evaluation
  • Application
  • Summary of Sign Properties
the unit circle
The Unit Circle

If a point (a,b) lies on the unit circle, then the following are true for the angle x associated with that point:

sin x = b

cos x = a

tan x = b/a (a ≠ 0)

csc x = 1/b (b ≠ 0)

sec x = 1/a (a ≠ 0)

cot x = a/b (b ≠ 0)

evaluating trigonometric functions
Evaluating Trigonometric Functions

Example:

Find the exact values of the 6 trigonometric functions for the point (-4, -3)

The Pythagorean Theorem shows that the distance from the point to the origin is 5.

sin x = -3/5

cos x = -4/5

tan x = 3/4

csc x = -5/3

sec x = -5/4

cot x = 4/3

using given information to evaluate trigonometric functions
Using Given Information to Evaluate Trigonometric Functions
  • Example:
  • Given that the terminal side of an angle is in Quadrant IV and cos x = 3/5 find the remaining trigonometric functions.
  • b2 = 25 – 9 = 16, so b = 4
  • Sin x = 4/5, tan x = -4/3, csc x = -5/4,
  • sec x = 5/3 and cot x = -3/4
calculator evaluation
Calculator Evaluation
  • Set the calculator in the proper mode for each method of evaluating trigonometric functions. Use degree mode or radian mode.
  • Example:

Find tan 3.472 rad

Solution: tan 3.472 rad ≈ .3430

  • Example:

Find csc 192º 47’ 22”

Solution: csc 192º 47’ 22” ≈

1/ sin 192.7894… ≈ -4.517

ad