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Mastering Cosine Angle Formulas: Application and Evaluation Techniques

This lesson focuses on the development and application of cosine formulas for angle operations. Students will learn to evaluate expressions involving cosine using identities for difference and sum of angles. Examples include evaluating cos(60° – 30°) and finding exact values for non-special angles like cos(75°). The lesson also covers scenarios where both angles are in the same or different quadrants, such as in Quadrant II and III. Assignments will reinforce concepts with practical exercises from pages 492 and 495.

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Mastering Cosine Angle Formulas: Application and Evaluation Techniques

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  1. Aim: How do we develop and apply the formula for cos (A B)? Do Now: Evaluate the following 1. cos (60° – 30°) 2. cos 60° cos 30° + sin 60° sin30° 3. cos(60° + 30°) 4. cos 60° cos 30° – sin 60° sin 30° HW: p.492 # 10,12,16,18 p.495 # 10,14,16,18

  2. Difference of two angles of cosine cos(A – B) = cos A cos B + sin A sin B Sum of two angles of cosine cos (A + B) = cos A cos B – sin A sin B

  3. We can use these formulas to find the exact values of non special angles Example: Find exact value of cos 75 cos 75 = cos(120 – 45) = cos 120 cos 45 +sin 120 sin 45 = • If Sin A = 3/5 with Example: in quadrant II and cos B = 5/13 with is in quadrant I, find cos (A – B). * First of all, find cos A and sin B cos A = – 4/5, sin B = 12/13 cos (A – B) = cos A cos B + sin A sin B = (- 4/5)(5/13) + (3/5)(12/13) = -20/65 + 36 /65 = 16/65

  4. Example: If is not in quadrant I ,and Is not in quadrant IV Find the value of

  5. APPLICATION: 1. Find the exact value of cos 15° 2. Use cos (A – B) to show cos(270° – x ) = – sin x 3. If and both A and B are in quadrant III. Find cos(A – B) 4. If Both angles are in quadrant III. Find the exact value of cos(x – y)

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