TEACHING OF TRIGONOMETRY

TLTCSP TOPIC 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

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.

PRACTICE ALGEBRAIC MANIPULATION

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.

LEARN BASIC GEOMETRY

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.

THREE SIDES OF RIGHT-ANGLED TRIANGLE

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.

THE THREE TRIGONOMETRIC RATIOS

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.

MOVE ON TO NON-RIGHT TRIANGLES

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.

LEARN TO MEASURE ANGLES IN RADIANS

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'.

OTHER THREE TRIGONOMETRIC RATIOS

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.

SOLVING TRIGONOMETRIC EQUATIONS

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.

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.

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

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

USEFUL RESOURCES

http://www.ies.co.jp/math/java/trig/

http://www.onlinemathlearning.com/basic-

trigonometry.html

http://www.wisc-

online.com/objects/ViewObject.aspx?ID=MS

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