6 5 basic trigonometric identities
This presentation is the property of its rightful owner.
Sponsored Links
1 / 16

6.5Basic Trigonometric Identities PowerPoint PPT Presentation


  • 111 Views
  • Uploaded on
  • Presentation posted in: General

6.5Basic Trigonometric Identities. Objective: Develop basic trigonometric identities. Trigonometric Identities. Trigonometric identities are equations that are true for all values of the variable for which the equation is defined. They are most often used to simplify an expression.

Download Presentation

6.5Basic Trigonometric Identities

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


6 5 basic trigonometric identities

6.5Basic Trigonometric Identities

Objective:

Develop basic trigonometric identities.


Trigonometric identities

Trigonometric Identities

  • Trigonometric identities are equations that are true for all values of the variable for which the equation is defined. They are most often used to simplify an expression.

  • Algebraic rules are the same for trigonometric expressions, the notation is sometimes just slightly different.


Quotient identities

Quotient Identities

  • In Chapter 6 we introduced the Unit Circle & we also learned our first identities:


Reciprocal identities

Reciprocal Identities

  • We also learned the reciprocal identities.


Example 1

Example #1

  • Simplify the following expressions:

    A)B)


Example 2

Example #2


Pythagorean identities

Pythagorean Identities

  • Using the Pythagorean Theorem & the Unit Circle, the Pythagorean Identities are created:


Pythagorean identities continued

Pythagorean Identities continued…

Be very careful when using Pythagorean identities, the expressions must be squared:


Example 3

Example #3

  • Simplify the following expressions.

    A)

This problem utilizes two identities:


Example 31

Example #3

  • Simplify the following expressions.

    B)

Two identities are also used here:


Example 4

Example #4

  • Use the Quotient, Reciprocal, and Pythagorean identities to find the remaining 5 trigonometric functions.


Periodicity identities

Periodicity Identities


Periodicity identities1

Periodicity Identities


Negative angle identities

Negative Angle Identities


Example 5

Example #5

  • Simplify the following expression.

This problem required first factoring the top and using the identity:

After the substitution, the bottom was factored and the top rearranged. Canceling like terms gives the answer shown.


Example 6

Example #6

  • Simplify the following expression.

Here the expression has a GCF factored out first. Then a substitution is made with this identity:

Then the reciprocal identity is used and like terms are canceled. Finally, the reciprocal identity is used again.


  • Login