1. 2/21/20161 1 Lesson 37 – Addition & Subtraction Identities PreCalculus - Santowski PreCalculus

2. 2/21/20162 Fast Five True or False (and justify your responses algebraically, graphically & numerically – but without the use of a calculator ) PreCalculus

3. 2/21/20163 (A) Six New Identities (GASP!!) Here are six new identities that we call the addition & subtraction identities 2/21/20163 PreCalculus

4. 2/21/20164 (B) Proving Cosine Subtraction Identity We will prove We will use our unit circle to do so..... http://www.cut-the- knot.org/triangle/SinCosFormula.shtml http://www.cut-the- knot.org/triangle/SinCosFormula.shtml 2/21/20164 PreCalculus

5. 2/21/20165 (C) Proving Sine Addition Identity We will prove We will use right triangle trig to do so http://www.cut-the- knot.org/triangle/SinCosFormula.shtml http://www.cut-the- knot.org/triangle/SinCosFormula.shtml 2/21/20165 PreCalculus

6. 2/21/20166 (D) Proving Tan Addition Identity You will prove You will use fundamental trig identities to do so 2/21/20166 PreCalculus

7. (E) Using the Addition/Subtraction Identities Evaluate each expression 1) sin (75°)  using sin (45° + 30°) 2) sin (75°)  using sin (120° – 45°) 3 ) cos (345°) 4) 2/21/2016 PreCalculus 7

8. 2/21/20168 (E) Using the Addition/Subtraction Identities Determine the exact value of sin(15º) Determine the exact value of cos(-195º) Determine the exact value of Determine the exact value of tan(255º) 2/21/20168 PreCalculus

9. Pop Quiz Find the exact value of 2/21/2016 PreCalculus 9

10. (E) Using the Addition/Subtraction Identities Find each of the following numbers: If 1) Evaluate sin (A + B) 2) Evaluate cos (A – B) 3) Evaluate tan (A + B) 4) If sin(a) = -4/5 for 180º<a<270º and if cos(b) = -5/13 for 90º<b<180º, evaluate tan(a+b) 2/21/2016 PreCalculus 10

11. (E) Using the Addition/Subtraction Identities Simplify the following: 2/21/2016 PreCalculus 11

12. 2/21/201612 (E) Using the Addition/Subtraction Identities We can use the new identities to develop new identities: Prove the following: (describe each identity from a transformations perspective as well as a unit circle perspective) 2/21/201612 PreCalculus

13. (E) Using the Addition/Subtraction Identities Find the exact value of: 2/21/2016 PreCalculus 13

14. 2/21/201614 (E) Using the Addition/Subtraction Identities Prove the following: 2/21/201614 PreCalculus

15. Solve for xER 2/21/2016 PreCalculus 15

16. Solve for xER 2/21/2016 PreCalculus 16

17. 2/21/201617 (E) Using the Addition/Subtraction Identities We can use the new identities to develop new identities: Develop a new identity for: (a) sin(2x) (b) cos(2x) (c) tan(2x) 2/21/201617 PreCalculus

18. Linear Combinations of Sine and Cosine 2/21/2016 PreCalculus 18

19. 2/21/201619 (F) Homework S14.4, p914, Q11,13,25,27,33-44all,67,77,78 2/21/201619 PreCalculus