Mr. Owh

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

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. 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. For right triangles the sineof an angle is defined below: NC 75A:SINE B Memorize It: SOH c a A C b

5. For right triangles the cosineof an angle is defined below: NC 75B:COSINE B Memorize It: CAH c a A C b

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

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

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

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

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

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

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

13. Example 3:Set up the cosine, sine, and tangent ratios of the given angle, then solve for x and y. x 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 y 15 Memorize It: SOH-CAH-TOA (so-ca-toe)

14. Have a great Spring Break! HW G2 #16 (Due Tue 4/18) Page 562 {3–15, 17–27 odd, 28–38, 48–51, 53, 54} Copy Problems & Figures !!! See you in a week!