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Unit 3: Trigonometric Identities

Test TUESDAY 3/11. Unit 3: Trigonometric Identities. MM4A5 . 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.

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Unit 3: Trigonometric Identities

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  1. Test TUESDAY 3/11 Unit 3: Trigonometric Identities MM4A5. 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. 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

  3. 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

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

  5. Booklet pg 2 Quotient Identities

  6. Booklet pgs 3-4 Pythagorean Identities ONLY WORK IN THIS FORMAT!

  7. Booklet pg 5 Sum and Difference Identities

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

  9. Booklet (back cover) Problem Solving Strategies • Convert everything to sines and cosines • Add fractions (find an LCD) • Create a monomial denominator • Split numerator • 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!

  10. Verifying The Identities on your HW

  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. Ticket out the Door • Turn in on your way out. TRY SOMETHING! Do NOT turn in a blank paper! • Complete the homework sheet (matching)

  15. 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

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

  17. Homework Questions?

  18. Simplify:

  19. Simplify

  20. Simplify

  21. Simplify

  22. Class work: Simplifying 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 

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