2. STEPS IN TEACHING TRIGONOMETRY
Brush up basic mathematical skills
Right-angled triangles and the three
trigonometric ratios
Non-right triangles, The Sine Rule, and The
Cosine Rule
Measure angles in radians
The other three trigonometric ratios
Solving trigonometric equations
3. PRACTICE ALGEBRAIC MANIPULATION
Algebraic manipulation is a very basic skill
that is necessary to study any branch of
mathematics.
Learn to change the subject of any equation.
Learn to solve linear and quadratic
equations.
Learn to solve simultaneous linear equations
and linear/quadratic pairs of simultaneous
equations.
5. LEARN BASIC GEOMETRY
Geometry is very closely related to
trigonometry and plays a vital part in solving
trigonometric problems.
Learn the properties of a circle.
Learn the properties of the interior and
exterior angles of polygons including
triangles.
Learn the three different types of triangles i.e.
isosceles, equilateral, and scalene.
7. THREE SIDES OF RIGHT-ANGLED TRIANGLE
The hypotenuse is the side opposite the right
angle. It is the biggest side of any right
triangle.
The two other sides are called the legs of the
triangle.
If you pick any angle in the triangle (besides
the right angle), you will see that one leg is
adjacent to the angle, and the other leg is
opposite the angle.
9. THE THREE TRIGONOMETRIC RATIOS
The Sine of any angle is the ratio of the length
of the side opposite it to the length of the
hypotenuse.
The Cosine of any angle is the ratio of the
length of the side adjacent to it to the length of
the hypotenuse.
The Tangent of any angle is the ratio of the Sine
of the angle to the Cosine of the angle. It is
often also taken as the ratio of the opposite to
the adjacent.
11. MOVE ON TO NON-RIGHT TRIANGLES
Because non-right triangles do not have a
right angle, the three trigonometric ratios play
a smaller role here.
Rather, two other rules become very
important: The Sine Rule, and The Cosine
Rule.
13. LEARN TO MEASURE ANGLES IN RADIANS
Radians are an alternate to degrees as a
way of measuring angles.
In 180o, there are pi, or approximately 3.142,
radians.
Radians are especially useful when it comes
to investigating the properties of a circle, and
are also used in physics in the study of
waves and simple harmonic motion.
15. OTHER THREE TRIGONOMETRIC RATIOS
Cosecant. It is the reciprocal of the sine i.e.
1/sin commonly called 'cosec' or 'csc'.
Secant. It is the reciprocal of the cosine
commonly called 'sec'.
Cotangent. It is the reciprocal of the tangent
commonly called 'cot'.
17. SOLVING TRIGONOMETRIC EQUATIONS
Trigonometric equations are equations
involving trigonometric functions.
Trigonometric equations can usually be
solved by manipulating the equation to
contain only one trigonometric ratio.
19. TIPS ON TEACHING TRIGONOMETRY
Review algebra and geometry, especially if
your students are weak.
Use a protractor.
Use a scientific calculator.
Remember that mathematics is a way of
thinking, not a bunch of formula to learn.
Develop your concepts and sharpen your
thinking skills through solving problems.
20. TASK: WORK IN PAIRS
Try to identify topic(s) in school trigonometry
perceived difficult to learn and why.
Propose a way to teach the topic(s) assumed
will overcome the difficulties.
Compare the difference of the Indonesian
syllabus to the Singaporean’s one on
Trigonometry.
21. LEARNING DIFFICULTIES
So many formulas to remember in
Trigonometry
Confused which one fix to use in solving a
problem
Misconception on algebraic properties of
trigonometric forms.
The most difficult one is the way and in what
condition they can apply their knowledge
22. OVERCOMING THE DIFFICULTIES
practiced in routine exercises to make them
memorized most part of the formulas such
that they can retrieve formula needed
automatically when solving certain problems.
get them involved to experience how the
knowledge is constructed and applied.
arrange the learning environment such that
the students could learn materials as realistic
as possible
Most of the students feel that there are so many formulas to remember in Trigonometry. It makes them frequently feel confused which one fix to use in solving a problem. In addition, they always have misconception on algebraic properties of trigonometric forms. For example, they frequently write sin 2x to be equal to 2 sin x. Moreover some of them also consider that sin2x equals to sin 2x. The most difficult one for them is the way and in what condition they can apply their knowledge.
