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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
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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
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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
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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
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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
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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
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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
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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
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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
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Text book
Calculator
Worksheets
Instructions and sheets of paper to produce the protractor
6. Assessment
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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