Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Date: 5.4(a) Notes: Sum and Difference Formulas Lesson Objective: Use sum and difference formulas to evaluate trig functions and verify identities. CCSS: F-TF Extend the domain of trigonometric functions using the unit circle. You will need: your trig identities cheat sheet Lesson 1: Cosine of the Sum of 2 Angles Use a graphing utility to graph y1 = cos(x + 2) and y2 = cos x + cos 2 in the same viewing window. What can you conclude about the graphs? Is it true that cos(x + 2) = cos x + cos 2? Lesson 1: Cosine of the Sum of 2 Angles 1. cos(u + v) = cos u cos v – sin u sin v Derived from the distance formula (see p. 424 for the proof); can be used to find the exact value of the cosine of any angle. Lesson 1: Cosine of the Sum of 2 Angles 1. cos(u + v) = cos u cos v – sin u sin v Derived from the distance formula (see p. 424 for the proof); can be used to find the exact value of the cosine of any angle. How can we remember this formula? There will actually be 5 more to add to this one. Lesson 1: Cosine of the Sum of 2 Angles 1. cos(u + v) = cos u cos v – sin u sin v Find the exact value of cos 105°. Lesson 2: The Rest of the Sum & Diff Formulas 1. cos(u + v) = cos u cos v – sin u sin v 2. cos(u – v) = cos u cos v + sin u sin v Lesson 2: The Rest of the Sum & Diff Formulas 1. cos(u + v) = cos u cos v – sin u sin v 2. cos(u – v) = cos u cos v + sin u sin v 3. sin(u + v) = sin u cos v + cos u sin v 4. sin(u – v) = sin u cos v – cos u sin v Lesson 2: The Rest of the Sum & Diff Formulas 1. cos(u + v) = cos u cos v – sin u sin v 2. cos(u – v) = cos u cos v + sin u sin v 3. sin(u + v) = sin u cos v + cos u sin v 4. sin(u – v) = sin u cos v – cos u sin v 5. tan(u + v) = tan u + tan v 1 – tan u tan v 6. tan(u – v) = tan u – tan v 1 + tan u tan v Lesson 3: Evaluating a Trig Expression Find the exact value of sin 5π . 12 Lesson 4: Evaluating a Trig Expression Find the exact value of cot(u + v) given sin u = and cos v = - 3 , 5 where both angles are in QII. 5 13 Lesson 5: Finding the Exact Value in Reverse Find the exact value. A. cos 70° cos 40° + sin70° sin 40° Lesson 5: Finding the Exact Value in Reverse Find the exact value. B. sin 3x cos 2y + cos 3x sin 2y 5.4(a): Do I Get It? Yes or No Find the exact value. 1. cos 75° π 2. sin 12 3. Find the exact value of csc(u – v) given sin u 5 3 = and cos v = - , where both angles are 13 5 in QII. 4. sin 42° cos 12° – cos 42° sin 12° 5. cos 3 cos 1.2 – sin 3 sin 1.2