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7-3A Trigonometric Ratios

7-3A Trigonometric Ratios. What is trigonometry? What is sine? What is cosine? What is tangent?. Definition. Trigonometry—the study of the special relationships between the angle measures and the side lengths of right triangles.

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7-3A Trigonometric Ratios

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  1. 7-3A Trigonometric Ratios What is trigonometry? What is sine? What is cosine? What is tangent?

  2. Definition Trigonometry—the study of the special relationships between the angle measures and the side lengths of right triangles. Trigonometric ratios are ratios of side lengths in right triangles.

  3. B A C Right triangle parts. hypotenuse leg leg Name the hypotenuse. Name the legs.

  4. Opposite or Adjacent? west • The opposite of east is ______ • The door is opposite the windows. • In a ROY G BIV, red is adjacent to _____ • The door is adjacent to the cabinet. orange

  5. B A C Triangle Parts Opposite side hypotenuse Adjacent side c Looking from angle B: Which side is the opposite? Which side is the adjacent? a b a b Opposite side Adjacent side Looking from angle A: Which side is the hypotenuse? Which side is the opposite? Which side is the adjacent? c a b

  6. B c a b A C Trigonometric ratios

  7. B c a b A C Trigonometric ratios and definition abbreviations SOHCAHTOA

  8. J L K Express each trig ratio as a fraction 13 5 12 sin L sin J cos L tan J SOHCAHTOA

  9. Using a scientific calculator to find the value of a trig ratio for an angle Calculators must first be in degree mode for trig values. If your calculator is not in degree mode, raise your hand. Graphing calculators need to be changed to degrees.

  10. Find the cos of 58° Enter: 58 cos = Enter: cos 58 =

  11. Z y x 42° X Y 15 Find the values of x and y What are the sides from angle Y? opp adj hyp 15 sin 42° = y y ≈ 10.04 15 cos 42° = x x ≈ 11.14717238≈11.15 SOHCAHTOA

  12. 70° y x 26 hyp Find x and y adj opp SOHCAHTOA

  13. What is trigonometry? The study of the special relationships between the angle measures and the side lengths of right triangles. What is sine? Side opposite over hypotenuse. What is cosine? Side adjacent over hypotenuse. What is tangent? Side opposite over side adjacent.

  14. Assignment 7-3A Page 514, 1-15

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