DEMO MELVIN E. CARNECER mathematics.pptx

For Mathematics

1. What Have I Learned

2. R_ _ _T

3. T_I_ _ _ _E

4. Right Triangle 1. Right Triangle- It is a triangle that contains a 90-degree angle or what is called a right angle.

5. _ E _ _

6. Legs 2. Legs – the two other sides of a right triangle which are shorter than the hypotenuse.

7. Hypotenuse 3. Hypotenuse – the longest side of a right triangle, which is the side opposite the right angle.

8. _PP_S _T_

9. Opposite 4. Opposite- It is the side across the given angle

10. Adjacent 5. Adjacent- It is the non-hypotenuse side next to the given angle

11. _ _ _L_

12. Given/Reference Angle 6. Given/Reference Angle- an acute angle that will serve as basis in identifying the opposite and adjacent side.

13. G_E_K A_PH_ _E_

14.   7. (theta)- one of the 24 greek alphabets customarily designated as variables that represents angular position of a vector  

15. _RIG_NO_E_RY

16. 8. Trigonometry- a branch of mathematics dealing with the relations of the sides and angles of a triangle. Trigonometry is derive from the greek word “trigon” which means triangle and ”metric” which means measurement. It is very important for an individual to learn, as it plays a vital role in construction, navigation, measuring , and many more.

17. Father of Trigonometry

18. Hipparchus of Nicea- a greek astronomer and matthematician who made fundamental contributions to the advancement of astronomy as a mathematical science and to the foundation of trigonometry.

19. Muhammad ibn Musa al-Khwarizmi- a Persian polymath and is considered as the Father of algebra and trigonometry of the muslim world.

20. TRIGONOMETRIC RATIOS

21. Competency & Objectives Illustrates the six trigonometric ratios: sine, cosine, tangent, secant, cosecant, and cotangent. (M9GE-IVa-1)

22. At the end of the lesson, you are expected to: • Identify the parts of a right triangle specially the given angle, hypotenuse, opposite, and adjacent side; • Apply the six trigonometric ratios in solving right triangles ; and • Relate the concepts on the six trigonometric ratios in solving real-life problems.

23. Ikaw na ba si Mr. Right? Instruction: Step 1: Students will be divided into four and shall be provided with rulers, protractors, paper, and pencils. Step 2: Your task is to draw and construct several right-angled triangles of different sizes on your paper using rulers to ensure the sides are straight and of varying lengths.

24. Step 3: After which the you will have to measure the lengths of the two shorter sides of each triangle using rulers and protractors to measure the acute angle between these sides. Then calculate the sine, cosine, and tangent ratios of angle for each triangle you construct.

25. Trigonometric Ratios- are special measurements of a right triangle or the ratios of the sides of a right triangle.

26. given angle right angle The Six Trigonometric Ratios

27. csc sec cot    

28. SOH – CAH – TOA is a mnemonic used for remembering the equations.

29. Showing a formula for the Missing Parts of a Right Triangle Example 2: Determine the equation or formula to find a missing part of the triangle.

30. Step 4: Bring the groups together to discuss their findings. Compare the values of sine, cosine, and tangent ratios for different triangles. Identify any patterns or relationships between the ratios and the size of the triangles or the angles. Discuss any discrepancies or interesting observations they made during the activity.

31. 1. How did you find our activity today? 2. How did the size of the triangle affect the values of sine, cosine, and tangent ratios? 3. What happens to the ratios when the angle θ changes? 4. How accurate were your measurements and calculations compared to theoretical values?

32. 1. What is trigonometric ratio? 2. What are the six trigonometric ratios? 3. What is trigonometry? 4. Who is the father of trigonometry? 5. What are the parts of a triangle?

33. Application Instruction: With the use of similar groupings, you will answer a real-life problem involving trigonometric ratios. 1. While playing, your slipper was stuck on a tree, you observe that 5 meters from the tree the angle of elevation from the ground is 45°. How tall must the ladder be in order to get your slippers?

34. ASSESSMENT

35. Direction: Solve and answer each items accurately and honestly. Given the figure below, find the following: cos β  

36. 2. Find the value of the following trigonometric ratios: sin θ  

37. Assignment What areas/fields of specialization in which trigonometry/trigonometric ratios plays an important role?

38. “If you are looking at anything from one point, from one angle, you can never attain wisdom because wisdom is to see all the things from every point, from every angle.” - Mehmet Murat Ildan

39. THANK YOU FOR LISTENING