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trigonometry

Find trigonometric ratios using right triangles. Solve problems using trigonometric ratios. trigonometry. trigonometric ratio sine cosine tangent.

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trigonometry

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  1. Find trigonometric ratios using right triangles. • Solve problems using trigonometric ratios. • trigonometry • trigonometric ratio • sine • cosine • tangent

  2. G.1 The student understands the structure of, and relationships within, an axiomatic system. (B)Recognize the historical development of geometric systems and know mathematics is developed for a variety of purposes. G.11 The student applies the concepts of similarity to justify properties of figures and solve problems. (C)Develop, apply, andjustify triangle similarity relationships, such asright triangle ratios,trigonometric ratios,and Pythagorean triples using a variety of methods.

  3. Find Sine, Cosine, and Tangent Ratios Find sin L, cos L, tan L, sin N, cos N, and tan N. Express each ratio as a fraction and as a decimal.

  4. Find Sine, Cosine, and Tangent Ratios

  5. Find Sine, Cosine, and Tangent Ratios

  6. Find Sine, Cosine, and Tangent Ratios

  7. Find Sine, Cosine, and Tangent Ratios Answer:

  8. A. B. C. D. Lesson 4 CYP1 A. Find sin A. • A • B • C • D

  9. A. B. C. D. Lesson 4 CYP1 B. Find cos A. • A • B • C • D

  10. A. B. C. D. Lesson 4 CYP1 C. Find tan A. • A • B • C • D

  11. A. B. C. D. Lesson 4 CYP1 D. Find sin B. • A • B • C • D

  12. A. B. C. D. Lesson 4 CYP1 E. Find cos B. • A • B • C • D

  13. A. B. C. D. Lesson 4 CYP1 F. Find tan B. • A • B • C • D

  14. KEYSTROKES:56 1.482560969 TAN ENTER Use a Calculator to Evaluate Expressions A. Use a calculator to find tan 56° to the nearest ten thousandth. Answer: tan 56° ≈ 1.4826

  15. KEYSTROKES:89 0.071452406 COS ENTER Use a Calculator to Evaluate Expressions B. Use a calculator to find cos 89° to the nearest ten-thousandth. Answer: cos 89° ≈ 0.0715

  16. Lesson 4 CYP2 A. Use a calculator to find sin 48° to the nearest thousandth. • A • B • C • D A.0.669 B.1.111 C.0.743 D.0.731

  17. Lesson 4 CYP2 B. Use a calculator to find cos 85° to the nearest ten thousandth. • A • B • C • D A. 0.0872 B. 0.9962 C. 11.4301 D. 0.0698

  18. Use Trigonometric Ratios to Find a Length EXERCISING A fitness trainer sets the incline on a treadmill to 7°. The walking surface is 5 feet long. Approximately how many inches did the trainer raise the end of the treadmill from the floor? Let y be the height of the treadmill from the floor in inches. The length of the treadmill is 5 feet, or 60 inches.

  19. KEYSTROKES: 607 7.312160604 SIN ENTER Use Trigonometric Ratios to Find a Length Multiply each side by 60. Use a calculator to find y. Answer: The treadmill is about 7.3 inches high.

  20. Lesson 4 CYP3 CONSTRUCTION The bottom of a handicap ramp is 15 feet from the entrance of a building. If the angle of the ramp is about 4.8°, how high does the ramp rise off the ground to the nearest inch? • A • B • C • D A. 1 in. B. 11 in. C. 16 in. D. 15 in.

  21. Use Trigonometric Ratios to Find an Angle Measure COORDINATE GEOMETRY Find mX in right ΔXYZ for X(–2, 8), Y(–6, 4), and Z(–3, 1).

  22. ExploreYou know the coordinates of the vertices of a right triangle and that is the right angle. You need to find the measures of one of the angles. PlanUse the Distance Formula to find the measure of each side. Then use one of the trigonometric ratios to write an equation. Use the inverse to find Solve or Use Trigonometric Ratios to Find an Angle Measure

  23. or or Use Trigonometric Ratios to Find an Angle Measure

  24. Use Trigonometric Ratios to Find an Angle Measure Use the cosine ratio. Simplify. Solve for x.

  25. Use a calculator to find ÷ ) 2ND KEYSTROKES:4 5 ENTER Use Trigonometric Ratios to Find an Angle Measure ExamineUse the sine ratio to check the answer. Simplify.

  26. ÷ ) 2ND KEYSTROKES:3 5 ENTER Use Trigonometric Ratios to Find an Angle Measure Answer: The measure of X is about 36.9.

  27. Lesson 4 CYP4 COORDINATE GEOMETRY Find mA in right ΔABC to the nearest degree. • A • B • C • D A. 66.0° B. 56.3° C. 33.7° D. 24.0°

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