Chapter 7 analytic trigonometry
This presentation is the property of its rightful owner.
Sponsored Links
1 / 17

Section 7.3 Double-Angle, Half-Angle, and Product-Sum Formulas PowerPoint PPT Presentation


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

Chapter 7 – Analytic Trigonometry. Section 7.3 Double-Angle, Half-Angle, and Product-Sum Formulas. Double Angle Formulas. The double-angle formulas allow us to find the values of the trigonometric functions at 2 x from their values at x. Proofs of Double Angle Formulas.

Download Presentation

Section 7.3 Double-Angle, Half-Angle, and Product-Sum Formulas

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


Chapter 7 analytic trigonometry

Chapter 7 – Analytic Trigonometry

Section 7.3 Double-Angle, Half-Angle, and Product-Sum Formulas

7.3 - Double-Angle, Half-Angle, and Product-Sum Formulas


Double angle formulas

Double Angle Formulas

  • The double-angle formulas allow us to find the values of the trigonometric functions at 2x from their values at x.

7.3 - Double-Angle, Half-Angle, and Product-Sum Formulas


Proofs of double angle formulas

Proofs of Double Angle Formulas

Now, you try the proof for cos2 and tan 2.

7.3 - Double-Angle, Half-Angle, and Product-Sum Formulas


Example

Example

  • If and  lies in quadrant II, find the exact value of each of the following:

7.3 - Double-Angle, Half-Angle, and Product-Sum Formulas


Example1

Example

  • Find the exact value of

7.3 - Double-Angle, Half-Angle, and Product-Sum Formulas


Power reducing formulas

Power Reducing Formulas

  • The power reducing formulas play an important part in calculus.

7.3 - Double-Angle, Half-Angle, and Product-Sum Formulas


Half angle formulas

Half Angle Formulas

  • NOTE: The choice of the + or – sign depends on the quadrant in which u/2 lies.

7.3 - Double-Angle, Half-Angle, and Product-Sum Formulas


Example2

Example

  • Find the exact value of cos105o.

7.3 - Double-Angle, Half-Angle, and Product-Sum Formulas


Example3

Example

Verify the identity:

7.3 - Double-Angle, Half-Angle, and Product-Sum Formulas


Example4

Example

Verify the identity:

7.3 - Double-Angle, Half-Angle, and Product-Sum Formulas


Product to sum formulas

Product-to-Sum Formulas

7.3 - Double-Angle, Half-Angle, and Product-Sum Formulas


Examples pg 515

Examples – pg. 515

  • Write the product as a sum.

7.3 - Double-Angle, Half-Angle, and Product-Sum Formulas


Sum to product formulas

Sum-to-Product Formulas

7.3 - Double-Angle, Half-Angle, and Product-Sum Formulas


Examples pg 5151

Examples – pg. 515

  • Write the product as a sum.

7.3 - Double-Angle, Half-Angle, and Product-Sum Formulas


Example pg 515

Example – pg. 515

  • Prove the identity.

7.3 - Double-Angle, Half-Angle, and Product-Sum Formulas


Example5

Example

  • Write an equivalent expression for cos4x that does not contain powers of trigonometric functions greater than 1.

7.3 - Double-Angle, Half-Angle, and Product-Sum Formulas


More examples

More Examples

  • Prove the identity.

7.3 - Double-Angle, Half-Angle, and Product-Sum Formulas


  • Login