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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.

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Presentation on theme: "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."— Presentation transcript:

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 = 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/ 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 / sin 27  = x 38 (0.4539) = x  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 / cos 27  = y 38 (0.8910) = y  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 / cos 42  = x x  sin 42  = y / sin 42  = y y  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 !!!


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