Lesson 51 Addition Subtraction Identities Math 2 Honors

Lesson 51 – Addition & Subtraction Identities Math 2 Honors - Santowski 1/1/2022 IB Math SL 1 - Santowski 1

Fast Five n True or False (and justify your response) n (a) sin(A + B) = sin. A + sin. B n (b) cos(A – B) = cos. A – cos. B 1/1/2022 IB Math SL 1 - Santowski 2

(A) Six New Identities (GASP!!) n Here are six new identities that we call the addition & subtraction identities 1/1/2022 IB Math SL 1 - Santowski 3

(B) Proving Cosine Subtraction Identity n We will prove n We will use our unit circle to do so. . . http: //www. cut-theknot. org/triangle/Sin. Cos. Formula. shtml n 1/1/2022 IB Math SL 1 - Santowski 4

(C) Proving Sine Addition Identity n We will prove n We will use right triangle trig to do so n http: //www. cut-theknot. org/triangle/Sin. Cos. Formula. shtml 1/1/2022 IB Math SL 1 –- Santowski 5

(D) Proving Tan Addition Identity n You will prove n You will use fundamental trig identities to do so 1/1/2022 IB Math SL 1 - Santowski 6

(E) Using the Addition/Subtraction Identities n Determine the exact value of sin(15º) n Determine the exact value of cos(-195º) n Determine the exact value of tan(255º) n If sin(a) = -4/5 for 180º<a<270º and if cos(b) = -5/13 for 90º<b<180º, evaluate tan(a+b) 1/1/2022 IB Math SL 1 - Santowski 7

(E) Using the Addition/Subtraction Identities n We can use the new identities to develop new identities: n Prove the following: (describe each identity from a transformations perspective as well as a unit circle perspective) 1/1/2022 IB Math SL 1 - Santowski 8

(E) Using the Addition/Subtraction Identities n Prove the following: 1/1/2022 IB Math SL 1 - Santowski 9

(E) Using the Addition/Subtraction Identities n We can use the new identities to develop new identities: n Develop a new identity for: n (a) sin(2 x) (b) cos(2 x) (c) tan(2 x) n n 1/1/2022 IB Math SL 1 - Santowski 10

(F) Homework n S 14. 4, p 914, Q 11, 13, 25, 27, 33 -44 all, 67, 78 1/1/2022 IB Math SL 1 - Santowski 11