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# Tltclsp topic 2

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• 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.
• ### Tltclsp topic 2

1. 1. TEACHING OF TRIGONOMETRYTLTCSP TOPIC 2
2. 2. STEPS IN TEACHING TRIGONOMETRY Brush up basic mathematical skills Right-angled triangles and the threetrigonometric ratios Non-right triangles, The Sine Rule, and TheCosine Rule Measure angles in radians The other three trigonometric ratios Solving trigonometric equations
3. 3. PRACTICE ALGEBRAIC MANIPULATION Algebraic manipulation is a very basic skillthat is necessary to study any branch ofmathematics. Learn to change the subject of any equation. Learn to solve linear and quadraticequations. Learn to solve simultaneous linear equationsand linear/quadratic pairs of simultaneousequations.
4. 4. PRACTICE ALGEBRAIC MANIPULATION
5. 5. LEARN BASIC GEOMETRY Geometry is very closely related totrigonometry and plays a vital part in solvingtrigonometric problems. Learn the properties of a circle. Learn the properties of the interior andexterior angles of polygons includingtriangles. Learn the three different types of triangles i.e.isosceles, equilateral, and scalene.
6. 6. LEARN BASIC GEOMETRY
7. 7. THREE SIDES OF RIGHT-ANGLED TRIANGLE The hypotenuse is the side opposite the rightangle. It is the biggest side of any righttriangle. The two other sides are called the legs of thetriangle. If you pick any angle in the triangle (besidesthe right angle), you will see that one leg isadjacent to the angle, and the other leg isopposite the angle.
8. 8. THREE SIDES OF RIGHT-ANGLED TRIANGLE
9. 9. THE THREE TRIGONOMETRIC RATIOS The Sine of any angle is the ratio of the lengthof the side opposite it to the length of thehypotenuse. The Cosine of any angle is the ratio of thelength of the side adjacent to it to the length ofthe hypotenuse. The Tangent of any angle is the ratio of the Sineof the angle to the Cosine of the angle. It isoften also taken as the ratio of the opposite tothe adjacent.
10. 10. THE THREE TRIGONOMETRIC RATIOS
11. 11. MOVE ON TO NON-RIGHT TRIANGLES Because non-right triangles do not have aright angle, the three trigonometric ratios playa smaller role here. Rather, two other rules become veryimportant: The Sine Rule, and The CosineRule.
12. 12. MOVE ON TO NON-RIGHT TRIANGLES
13. 13. LEARN TO MEASURE ANGLES IN RADIANS Radians are an alternate to degrees as away of measuring angles. In 180o, there are pi, or approximately 3.142,radians. Radians are especially useful when it comesto investigating the properties of a circle, andare also used in physics in the study ofwaves and simple harmonic motion.
14. 14. LEARN TO MEASURE ANGLES IN RADIANS
15. 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 cosinecommonly called sec. Cotangent. It is the reciprocal of the tangentcommonly called cot.
16. 16. OTHER THREE TRIGONOMETRIC RATIOS
17. 17. SOLVING TRIGONOMETRIC EQUATIONS Trigonometric equations are equationsinvolving trigonometric functions. Trigonometric equations can usually besolved by manipulating the equation tocontain only one trigonometric ratio.
18. 18. SOLVING TRIGONOMETRIC EQUATIONS
19. 19. TIPS ON TEACHING TRIGONOMETRY Review algebra and geometry, especially ifyour students are weak. Use a protractor. Use a scientific calculator. Remember that mathematics is a way ofthinking, not a bunch of formula to learn. Develop your concepts and sharpen yourthinking skills through solving problems.
20. 20. TASK: WORK IN PAIRS Try to identify topic(s) in school trigonometryperceived difficult to learn and why. Propose a way to teach the topic(s) assumedwill overcome the difficulties. Compare the difference of the Indonesiansyllabus to the Singaporean’s one onTrigonometry.
21. 21. LEARNING DIFFICULTIES So many formulas to remember inTrigonometry Confused which one fix to use in solving aproblem Misconception on algebraic properties oftrigonometric forms. The most difficult one is the way and in whatcondition they can apply their knowledge
22. 22. OVERCOMING THE DIFFICULTIES practiced in routine exercises to make themmemorized most part of the formulas suchthat they can retrieve formula neededautomatically when solving certain problems. get them involved to experience how theknowledge is constructed and applied. arrange the learning environment such thatthe students could learn materials as realisticas possible
23. 23. 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=MSR3603