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Lesson 19 Part 1 Pythagorean Theorem and the Primary Trigonometric Ratios Key Learning Goals • I can solve for missing sides and angles in right triangles using Pythagorean Theorem and the primary trigonometric ratios sine, cosine and tangent • I can identify and use the reciprocal trigonometric ratios cosecant, secant and cotangent • I can solve reallife problems using the six trigonometric ratios MINDS ON Accessing Our Prior Knowledge Pythagorean Theorem Practice. Solve for the missing side of each right triangle. A. B. MINDS ON Accessing Our Prior Knowledge The Primary Trigonometric Ratios There is a proportional relationship between a given angle in a right triangle and the length of the sides that make up that triangle. We will explore this relationship by examining right triangles with different values of the angle A. Activity: The Geometer's Sketchpad ACTION The Primary Trigonometric Ratios The three primary trigonometric ratios are sine, cosine and tangent. Each ratio compares the following pairs of sides. sine = opposite hypotenuse cosine = adjacent tangent = opposite hypotenuse adjacent SOHCAHTOA So for Δ ABC we have: sin A = sin B = cos A = cos B = tan A = tan B = Skill: Solving for a missing side in a right triangle using the primary trigonometric ratios. Example Find the value of the missing side in each triangle. Round to nearest tenth of a unit. A. B. C. Skill: Solving for a missing angle in a right triangle using the primary trigonometric ratios. Example Find the value of the missing angle in each triangle. Round to the nearest degree. A. B. C. Skill: Solving a right triangle using the primary trigonometric ratios. The Reciprocal Trigonometric Ratios The reciprocal trigonometric ratios are the reciprocals of the primary trigonometric ratios. Therefore the ratios are: cosecant = 1 = hypotenuse (csc) sine opposite secant = 1 = hypotenuse (sec) cosine adjacent cotangent = 1 = adjacent (cot) tangent opposite Practice For the triangle shown below identify the following ratios: sin P = csc P = cos P = sec P = tan P = cot P = Practice State the reciprocal ratios for triangle DEF. D E F Practice Given that cotθ = 6 , solve for θ. 5 Practice Given that cscθ = 8 , solve for θ. 3 Assigned Practice Section 5.1, p. 280282, #1, 3, 4, 6, 9 Worksheet