1. 1 Mr. Owh Today is: Friday, April 7 th, 2006 Lesson 9.5A – Trigonometric Ratios 75A, 75B, 75C, 75D, 76 75A, 75B, 75C, 75D, 76 Announcements: Chapter 9 is about Right Triangles & Trigonometry Chapter 9 Test is April 21. Extra Credit assignment.

2. 2 Lesson 9.5A – Trigonometric Ratios Today’s Objectives:  Find the sine, the cosine, and the tangent of an acute angle. Today’s Key Terms: sine, cosine, tangent Materials Needed Today: notebook, geometer/ruler, calculator Today’s Geometry Standards: 18, 19

3. 3 Trigonometry Trigonometry: Greek for “triangle measuring” Trigonometry is the study of special relationships between angle measures and side lengths of right triangles. The ratios are: SINE, COSINE, and TANGENT

4. 4 For right triangles the sine of an angle is defined below: NC 75A: SINE b c a B AC Memorize It: SOH

5. 5 For right triangles the cosine of an angle is defined below: NC 75B: COSINE b c a B AC Memorize It: CAH

6. 6 For right triangles the tangent of an angle is defined below: NC 75C: TANGENT b c a B AC Memorize It: TOA

7. 7 Trigonometric Ratios: NC 75D: b c a B AC Memorize It: SOH-CAH-TOA (so-ca-toe)

8. 8 Example 1: Express each trigonometric ratio as a fraction and as a decimal (hundredths place): Answer: sin J = sin L = cos J = cos L = tan J = tan L = 13 5 12 J KL Mr. Owh’s Tip: Use  J and  L & use SOH-CAH-TOA

9. 9 Example 1: Express each trigonometric ratio as a fraction and as a decimal (hundredths place): Answer: sin J = 12/13sin L = 5/13 cos J = 5/13cos L = 12/13 tan J = 12/5tan L = 5/12 13 5 12 J KL Mr. Owh’s Tip: Use  J and  L & use SOH-CAH-TOA

10. 10 Example 2: Set up the following ratios then solve for x and y. Answer: use sine sin 27  = x / 38 38 sin 27  = x 38 (0.4539) = x 17.252  x 38 x y N P M 27  Memorize It: SOH

11. 11 Example 2: Set up the following ratios then solve for x and y. Answer: use cosine cos 27  = y / 38 38 cos 27  = y 38 (0.8910) = y 33.858  y 38 x y N P M 27  Memorize It: CAH

12. 12 Example 2: Set up the following ratios then solve for x and y. Answer: use tangent tan 27   x / y 38 x y N P M 27  Memorize It: TOA

13. 13 Example 3: Set up the cosine, sine, and tangent ratios of the given angle, then solve for x and y. Answer: cos 42  = x / 15 15 cos 42  = x x  11.147 sin 42  = y / 15 15 sin 42  = y y  10.037 tan 42  = y / x 42  x 15 y Memorize It: SOH-CAH-TOA (so-ca-toe)

14. 14 HW G2 #16 (Due Tue 4/18) Page 562 {3–15, 17–27 odd, 28–38, 48–51, 53, 54} Copy Problems & Figures !!!