Lesson 23 Addition Subtraction Identities HL Math Santowski

Lesson 23 – Addition & Subtraction Identities HL Math - Santowski 12/21/2021 HL Math - Santowski 1

Fast Five n True or False (and justify your responses algebraically, graphically & numerically – but without the use of a calculator ) 12/21/2021 HL Math - Santowski 2

(A) Six New Identities (GASP!!) n Here are six new identities that we call the addition & subtraction identities 12/21/2021 HL Math - 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 12/21/2021 HL Math - 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 12/21/2021 HL Math - Santowski 5

(D) Proving Tan Addition Identity n You will prove n You will use fundamental trig identities to do so 12/21/2021 HL Math - Santowski 6

(E) Using the Addition/Subtraction Identities n Evaluate each expression n n 1) sin (75°) using sin (45° + 30°) 2) sin (75°) using sin (120° – 45°) 3) cos (345°) n 4) n 12/21/2021 HL Math - Santowski 7

(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) 12/21/2021 HL Math - Santowski 8

Pop Quiz n Find the exact value of 12/21/2021 HL Math - Santowski 9

(E) Using the Addition/Subtraction Identities n Find each of the following numbers: n If n 1) Evaluate sin (A + B) 2) Evaluate cos (A – B) 3) Evaluate tan (A + B) n n n 4) If sin(a) = -4/5 for 180º<a<270º and if cos(b) = -5/13 for 90º<b<180º, evaluate tan(a+b) 12/21/2021 HL Math - Santowski 10

(E) Using the Addition/Subtraction Identities n Simplify the following: 12/21/2021 HL Math - Santowski 11

(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) 12/21/2021 HL Math - Santowski 12

(E) Using the Addition/Subtraction Identities n Find the exact value of: 12/21/2021 HL Math - Santowski 13

(E) Using the Addition/Subtraction Identities n Prove the following: 12/21/2021 HL Math - Santowski 14

Solve for x. ER 12/21/2021 HL Math - Santowski 15

Solve for x. ER 12/21/2021 HL Math - Santowski 16

(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 12/21/2021 HL Math - Santowski 17

Linear Combinations of Sine and Cosine 12/21/2021 HL Math - Santowski 18