1 / 22

Unit 3: Trigonometric Identities

Test Thursday 12/6. Unit 3: Trigonometric Identities. MA3A5. Students will establish the identities and use them to simplify trigonometric expressions and verify equivalence statements. LG 3-1 Simplifying & Verifying Identities LG 3-2 Applying Trig Identities. Answer Key.

jason
Download Presentation

Unit 3: 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. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Test Thursday 12/6 Unit 3: Trigonometric Identities MA3A5. Students will establish the identities and use them to simplify trigonometric expressions and verify equivalence statements. LG 3-1 Simplifying & Verifying Identities LG 3-2 Applying Trig Identities

  2. Answer Key • Reciprocal Identities • Product Identities • Pythagorean Identities

  3. What is a trigonometric identity? • A trigonometric identity is a trigonometric equation that is valid for all values of the variables for which the expression is defined. • In this unit, you will be manipulating expressions to make them equal something • When simplifying, you won’t know the answer • When verifying, you have the answer and your job is to manipulate one side of an equation to make it look like the other side

  4. Unit 3: Trig Identities • You will now make a booklet with all the identities you are required to learn for this unit. • PLEASE PAY ATTENTION as we fold our booklets • On the FRONT COVER, write the title of the unit and YOUR NAME! • Do NOT lose your booklet! • Look for this symbol so you know when to write in your booklet Booklet

  5. Booklet pg 1 Reciprocal Identities Also work with powers…

  6. Booklet pg 2 Quotient Identities

  7. + 1 tan2 = sec2 cot2 + 1 = csc2 Booklet pgs 3-4 Pythagorean Identities cos2 + sin2 = 1

  8. Booklet pg 5 Sum and Difference Identities The identity above is a short hand method for writing two identities as one. When these identities are broken up, they look like: The identity above is a short hand method for writing two identities as one. When these identities are broken up, they look like:

  9. Booklet pg 6 Double-Angle Identities sin (2x) = 2sin x cos x cos(2x) = cos2x - sin2x = 2cos2x – 1 = 1 - 2sin2x

  10. Booklet (back cover) Problem Solving Strategies • Convert everything to sines and cosines • Add fractions (find an LCD) • Create a monomial denominator • Factor if possible • When verifying, work on ONE side only – always pick the more complicated side to transform • Always try SOMETHING! It may not be the right thing but it’s better than nothing!

  11. Example 1: Simplify sin x cot x Substitute using the quotient property. Simplify. Done!

  12. Example 2: Simplify Use the reciprocal and quotient properties to make fractions. Cancel the sines and cosines. Done!

  13. Example 3: Simplify:

  14. Warm UP! Which of the following expressions is equal to sin(x)? a. b. c. a. b. c. Which of the following expressions is equal to

  15. Ways to simplify/verify (or check your answers!) Algebraically Graphically Numerically a. b. c.

  16. Simplify

  17. Simplify

  18. Simplify

  19. Class work: Simplifying and Verifying Identities Worksheet You CAN work together You CAN use a marker on your desk You SHOULD raise your hand if you get stuck You SHOULD check your answers on your calc 

  20. Ticket out the Door… Verifying the following identity. Use your brain and your booklet only 

  21. Homework: Finish the worksheet Check the blog for videos DON’T LOSE YOUR BOOKLET! Happy Thanksgiving Break 

  22. Ticket out the Door… Verifying the following identity. Use your brain and your booklet only 

More Related