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Región de Murcia Consejería de Educación, Formación y Empleo D.G. de Planificación y Ordenación Educativa Trigonometry This is the 6th unit in the curriculum of Mathematics option B, a subject of 4th ESO. 6 lessons have been planned to teach that unit. The students are supposed to know the geometry of triangles and the sexagesimal system of angles measure, since these contents had been studied the previous years. The concept of similarity and the Thales theorem have been the subject of the 5th unit this year, so the students should know it too. 2. Objectives Understanding the different systems of measuring angles, and change the units by using the calculator Awareness of the relationship between sides and angles in right triangles. Expression of these relationships as trigonometric ratios and use of these ratios to solve geometric problems. 3. Contents Measure of angles. Sexagesimal degrees and radians. Change of units Trigometric ratios of acute angles. Sine, cosine and tangent. Determining the trigonometric ratios on angles in right triangles. Finding angles when the sides are known and finding sides as the angles are given Trigonometric ratios for 30º, 45º y 60º. Determining their exact values Relationship between the different trigonometric ratios of an angle. Working out one ratio of an angle as another ratio is given. 4. Lessons and activities Lesson 1.- Measure of angles. Use of the calculator o o o o Sexagesimal units Radians Operating with angles in both systems using the calculator Change from one system to the other one using the calculator Lesson 2.- Trigonometric ratios for acute angles o o o o Sine, cosine and tangent of an acute angle Properties of these ratios Using the calculator to find the sine, cosine otr tangent of a given angle Using the calculator to find an acute angle as either its sine, cosine or tangent is given Lesson 3.- Ratios for angles of 30º, 60º and 45º o o o o Exact value for the sine, cosine and tangent of 30º . Geometrical deduction Exact value for the sine, cosine and tangent of 60º . Geometrical deduction Exact value for the sine, cosine and tangent of 45º . Geometrical deduction Exact value for the sine, cosine and tangent of an acute angle in a right triangle, as two of its sides are given. Geometrical deduction Región de Murcia Consejería de Educación, Formación y Empleo D.G. de Planificación y Ordenación Educativa Lesson 4.- Relationship between different ratios o o The fundamental trigonometric equations. Relation between sine and cosine of an acute angle Relation between the sine, cosine and tangent of an acute angle Relation between the cosine and the tangent of an acute angle Using the formulae above to find the exact value for any of the ratios of an angle as one of the other ratios is given Lesson 5.- Solving right triangles o o Different right triangles are proposed and the students should find the unknown elements. The hypotenuse and one leg given (to find out the other leg and both acute angles) Both legs are given (to find out the hypotenuse and both acute angles) One leg and its opposite angle are given (to find out the hypotenuse, the other leg and the other angle) One angle and its adjacent leg are given (to find out the hypotenuse, the other leg and the other angle) The hypotenuse and one of the acute angles are given (to find out both legs and the other angle) The students would understand the importance of using the most adequate ratio for each case, so that the accuracy of the result is appropriate Lesson 6.- Pocket protractor o Using the knowledge of angles and its relations to produce a “pocket protractor” that will allow to measure some of the most common angles 8such as 30º, 15º, 45º, 60º, 75º, and so on. 5. Didactic Resources o o o o Text book Calculator Worksheets Instructions and sheets of paper to produce the protractor 6. Assessment o o o o Checking the activities proposed as a homework everyday Checking the class work everyday Evaluating the protractor once produced Proposing two exercises like the ones that have been done in the different lessons to check the ability of the students to solve them Amparo Ramírez de Arellano Sánchez Matemáticas