Trigonometry Ratios Grade 9 Mathematics.pptx

Trigonometry 9, Basic Trigonometry Ratios

1. Trigonometry: The Six Trigonometry Ratios Grade 9 Mathematics -Keizar Paul B. Gonzales Lesson 1

2. 01 Illustrate the six trigonometric ratios: sine, cosine, tangent, secant, cosecant, and cotangent; Objectives Introduction to Trigonometry Ratios: 02 Find the value of the six trigonometric ratios from the given triangle; and Unlocking Trigonometric Secrets: 03 Appreciate the importance of trigonometry in real life situations. Using Trigonometry in Everyday Contexts:

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8. Guide Questions What comes to your mind when you heard about triangles? In your opinion, How can trigonometry be used in surveying to measure distances and angles accurately when mapping land or constructing buildings? How ancient people discovered Trigonometry?

9. -Trigonometry is a branch of Mathematics that deals with the relation between the sides and angles of a triangle. - From the Greek words “ trigonon ” trigon meaning triangle and “ metron ”, to measure. It is literally means “ measurement of triangles ”. Trigonometry -It is a tool used for measuring distances that cannot be directly measured. - Trigonometry involves the study of angles and geometric ratios. Hipparchus Father of Trigonometry

10. Right Triangle Trigonometry It is often used to find the length of one side or the measure of an acute angle of a right triangle. Hypotenuse – is always the side opposite the right angle, it is the longest side of a right triangle. Adjacent side – the side which is also a side of the given acute angle. Opposite side – The side opposite the given acute angle.

11. Draw a Right Triangle: Sketch a right triangle with one angle labeled as θ (theta). Identify Adjacent and Opposite Sides: Adjacent Side: Touches angle θ but isn't the hypotenuse. (Sides 'a' or 'b' in the triangle) Opposite Side: Not one of the legs forming angle θ nor the hypotenuse. (Side 'c' in the triangle) Relate to Theta (θ): Adjacent side is next to θ. Opposite side is across from θ. How do you know which is Adjacent and Opposite? What is Theta (θ)? Theta (θ) is a symbol used to represent an angle in mathematics, particularly in geometry and trigonometry. It's like a placeholder for an unknown or specified angle in equations and diagrams.

12. Draw a Right Triangle: Sketch a right triangle with one angle labeled as θ (theta). Identify Adjacent and Opposite Sides: Adjacent Side: Touches angle θ but isn't the hypotenuse. (Sides 'a' or 'b' in the triangle) Opposite Side: Not one of the legs forming angle θ nor the hypotenuse. (Side 'c' in the triangle) Relate to Theta (θ): Adjacent side is next to θ. Opposite side is across from θ. Identifying the Adjacent and Opposite of a Right Triangle Hypotenuse Adjacent Opposite

13. Draw a Right Triangle: Sketch a right triangle with one angle labeled as θ (theta). Identify Adjacent and Opposite Sides: Adjacent Side: Touches angle θ but isn't the hypotenuse. (Sides 'a' or 'b' in the triangle) Opposite Side: Not one of the legs forming angle θ nor the hypotenuse. (Side 'c' in the triangle) Relate to Theta (θ): Adjacent side is next to θ. Opposite side is across from θ. Identifying the Adjacent and Opposite of a Right Triangle Hypotenuse

14. Draw a Right Triangle: Sketch a right triangle with one angle labeled as θ (theta). Identify Adjacent and Opposite Sides: Adjacent Side: Touches angle θ but isn't the hypotenuse. (Sides 'a' or 'b' in the triangle) Opposite Side: Not one of the legs forming angle θ nor the hypotenuse. (Side 'c' in the triangle) Relate to Theta (θ): Adjacent side is next to θ. Opposite side is across from θ. Identifying the Adjacent and Opposite of a Right Triangle Opposite Adjacent Hypotenuse

15. Draw a Right Triangle: Sketch a right triangle with one angle labeled as θ (theta). Identify Adjacent and Opposite Sides: Adjacent Side: Touches angle θ but isn't the hypotenuse. (Sides 'a' or 'b' in the triangle) Opposite Side: Not one of the legs forming angle θ nor the hypotenuse. (Side 'c' in the triangle) Relate to Theta (θ): Adjacent side is next to θ. Opposite side is across from θ. Identifying the Adjacent and Opposite of a Right Triangle Hypotenuse

16. Draw a Right Triangle: Sketch a right triangle with one angle labeled as θ (theta). Identify Adjacent and Opposite Sides: Adjacent Side: Touches angle θ but isn't the hypotenuse. (Sides 'a' or 'b' in the triangle) Opposite Side: Not one of the legs forming angle θ nor the hypotenuse. (Side 'c' in the triangle) Relate to Theta (θ): Adjacent side is next to θ. Opposite side is across from θ. Identifying the Adjacent and Opposite of a Right Triangle Hypotenuse Opposite Adjacent

17. Draw a Right Triangle: Sketch a right triangle with one angle labeled as θ (theta). Identify Adjacent and Opposite Sides: Adjacent Side: Touches angle θ but isn't the hypotenuse. (Sides 'a' or 'b' in the triangle) Opposite Side: Not one of the legs forming angle θ nor the hypotenuse. (Side 'c' in the triangle) Relate to Theta (θ): Adjacent side is next to θ. Opposite side is across from θ. Identifying the Adjacent and Opposite of a Right Triangle Hypotenuse

18. Draw a Right Triangle: Sketch a right triangle with one angle labeled as θ (theta). Identify Adjacent and Opposite Sides: Adjacent Side: Touches angle θ but isn't the hypotenuse. (Sides 'a' or 'b' in the triangle) Opposite Side: Not one of the legs forming angle θ nor the hypotenuse. (Side 'c' in the triangle) Relate to Theta (θ): Adjacent side is next to θ. Opposite side is across from θ. Identifying the Adjacent and Opposite of a Right Triangle Hypotenuse Opposite Adjacent

19. Identifying the Adjacent and Opposite of a Right Triangle Hypotenuse Draw a Right Triangle: Sketch a right triangle with one angle labeled as θ (theta). Identify Adjacent and Opposite Sides: Adjacent Side: Touches angle θ but isn't the hypotenuse. (Sides 'a' or 'b' in the triangle) Opposite Side: Not one of the legs forming angle θ nor the hypotenuse. (Side 'c' in the triangle) Relate to Theta (θ): Adjacent side is next to θ. Opposite side is across from θ.

20. Identifying the Adjacent and Opposite of a Right Triangle Hypotenuse Draw a Right Triangle: Sketch a right triangle with one angle labeled as θ (theta). Identify Adjacent and Opposite Sides: Adjacent Side: Touches angle θ but isn't the hypotenuse. (Sides 'a' or 'b' in the triangle) Opposite Side: Not one of the legs forming angle θ nor the hypotenuse. (Side 'c' in the triangle) Relate to Theta (θ): Adjacent side is next to θ. Opposite side is across from θ. Opposite Adjacent

21. Primary Trigonometry Ratios Sine (Sin) Cosine (Cos) Tangent (Tan) A B C a b c SOH-CAH-TOA            

22. Secondary Trigonometry Ratios Cosecant (Csc) Secant (Sec) Cotangent (Cot) A B C a b c In trigonometry, besides the primary trigonometric ratios (sine, cosine, and tangent), there are three secondary trigonometric ratios: cosecant, secant, and cotangent. These ratios are reciprocals of the primary ratios.       Reciprocal of Sine (Sin) Reciprocal of Cosine (Cos) Reciprocal of T angent (Tan)      

23. SOH-CAH-TOA S- Sine O – Opposite H- Hypothenuse C – Cosine A – Adjacent H – Hypothenuse T – Tangent O – Opposite A - Adjacent       Cosecant – Secant – Cotangent - Reciprocal of Sine (Sin) Reciprocal of Cosine (Cos) Reciprocal of T angent (Tan)      

24. Example 5 Remember the SOH-CAH-TOA Step 1. Identify where is the theta or Degree. 01   3 4 Step 2. Identify where is the Hypothenuse, Opposite, Adjacent. Step 3. Evaluate using SOH-CAH-TOA                        

25. Example 10 Remember the SOH-CAH-TOA Step 1. Identify where is the theta or Degree. 02   8 6 Step 2. Identify where is the Hypothenuse, Opposite, Adjacent. Step 3. Evaluate using SOH-CAH-TOA                        

26. Try This! 13 Remember the SOH-CAH-TOA Step 1. Identify where is the theta or Degree. 03   12 5 Step 2. Identify where is the Hypothenuse, Opposite, Adjacent. Step 3. Evaluate using SOH-CAH-TOA                        

27. Try This! 13 Remember the SOH-CAH-TOA Step 1. Identify where is the theta or Degree. 04 12 5 Step 2. Identify where is the Hypothenuse, Opposite, Adjacent. Step 3. Evaluate using SOH-CAH-TOA                        

28. Example x Remember the SOH-CAH-TOA Step 1. Identify where is the theta or Degree. 05 24 7 Step 2. Identify where is the Hypothenuse, Opposite, Adjacent. Step 3. Evaluate using SOH-CAH-TOA                         Step 3. find the missing value using Pythagorean Theorem             25

29. Example 06 x 3            

30. Example 06 3                                    

31. Example 06 3                                    

32. Example 06 3                                    

33. Assignment Make an acronym on a piece of Bond paper (any size) using the trigonometric functions (6): sine, cosine, tangent, cotangent, secant, and cosecant, that are related in Math. (No Short Cut) Example: (Do not copy the example) S- Statistics I- Imaginary Numbers N- Number Theory E- Exponential

34. —Keizar “Life is like a trigonometry, every degree has a different unique answer, but every situation it becomes theta, when you leave it, it still unknown for future situation.