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GEOMETRY MODULE 2 LESSON 27 SINE AND COSINE OF COMPLEMENTARY ANGLES AND SPECIAL ANGLES OPENING EXERCISE Complete Example 1 from your workbook. ο· Why do we know that alpha, πΌ and beta, π½ are complementary? The sum of all the angles in a triangle is 180°. Since angle C is the right angle, the sum of πΌ and π½ must be 90°. WORKBOOK Exercise 1 (Together) Consider the right triangle ABC so that β πΆ is a right angle, and the degree measures of β π΄ and β π΅ are πΌ and π½, respectively. a. Find πΌ + π½. πΌ + π½ = 90° π΅πΆ b. Use trigonometric ratios to describe π΄π΅ in two different ways. π΅πΆ π΅πΆ sin β π΄ = π΄π΅ , cos β π΅ = π΄π΅ c. Use trigonometric ratios to describe π΄πΆ π΄πΆ π΄π΅ in two different ways. π΄πΆ sin β π΅ = π΄π΅ , cos β π΄ = π΄π΅ d. What can you conclude about sin πΌ and cos π½? sin πΌ = cos π½ e. What can you conclude about cos πΌ and sin π½? cos πΌ = sin π½ MOD2 L27 1 ON YOUR OWN Complete Exercise 2 and 3 in your workbook. 2. a) π = 65 b) π = 10 c) π = 40 d) π = 67.5 3. Sine and cosine have the same value for π = 45. The sine of an angle is equal to the cosine of its complement. Since the complement of 45 is 45, sin 45 = cos 45. DISCUSSION http://www.rkm.com.au/ANIMATIONS/animation-Pythagoras-Theorem.html ο· What is happening to π and π as π changes? What happens to sin π and cos π? Let π = 1. o As π gets smaller approaching 0°, π π decreases. Since sin π = 1, sin π is approaching 0. π π increases. Since cos π = 1, sin π is approaching 1. o As π gets bigger approaching 90°, π π increases. Since sin π = 1, sin π is approaching 1. π π decreases. Since cos π = 1, sin π is approaching 0. EXAMPLE 3 a. Whatβs an easy way to remember the entries in the table? 1 β2 β3 , ,1 2 2 2 Consider the sequence 0, , or β0 1 β2 β3 β4 , , , , . 2 2 2 2 2 Apply the sequence left to right in the sine row then right to left in the cosine row. π½ Sine Cosine MOD2 L27 2 THE UNIT TRIANGLES Create a similar triangle. Choose a scale factor and apply through multiplication. Complete exercise 4 and 5 in your workbook. MOD2 L27 3 SUMMARY ο· The sine of an angle is equal to the cosine of its complementary angle, and the cosine of an angle is equal to the sine of its complementary angle. ο· Sine and Cosine for Special Angles: HOMEWORK Problem Set Module 2 Lesson 27, page 212 #1, 3, 4, 5: Show all work in an organized and linear manner. There is not enough room in the workbook. Present your homework on a separate sheet of paper. DUE: Tuesday, Jan 17, 2017 MOD2 L27 4