Trigonometry Presentation and Real Life Problem

Trigonometric ratios describe the relationship between the angles and sides of a right triangle, and there are 3 common trigonometric functions. Sine, cosine, and tangent. However, we also have their reciprocals which is the cosecant, secant, and cotangent.

1. Let’s recall: Pythagorean Theorem states that, “in a right-angled triangle, the square of the longest side is equal to the sum of squares of the other two sides.” a 2 + b 2 = c 2

2. Trigonometric Ratios for Right Triangles

3. At the end of the lesson, all of the learners must be able to: Distinguish and operate the six(6) trigonometric ratios on various right-angled triangles; Apply trigonometric ratios to solve for missing sides and angles in a right triangle; and Evaluate the applications of trigonometric ratios through real-world problem analysis and discussion.

4. Trigonometry Invented by the Greek mathematician and astronomer Hipparchus of Nicaea, who is now known as “The father of Trigonometry” It deals with the study of the relationship between the sides and angles of the right-angle triangle

5. The Trigonometric Ratios SOH – CAH – TOA SOH = Sine is opposite side over the hypotenuse side CAH = Cosine is adjacent side over the hypotenuse side TOA = Tangent is opposite side over the adjacent side

6. Pythagorean theorem Trigonometric Ratios

7. Reference Angle– is the non right-angle which is commonly denoted as 𝜃 (theta) Hypotenuse side – i s t he longest leg and always face the right angle opposite side – is t he side opposite the angle of interest adjacent side – is the one right next to the reference angle PARTS OF A RIGHT TRIANGLE

8. The angle of interest which is 37° The hypotenuse side which is 5 units The opposite side which is 3 units The adjacent side which is 4 units PARTS OF A RIGHT TRIANGLE

9. The 3 trigonometric functions are: Sine(sin), Cosine(cos), and Tangent(tan) The reciprocal of the 3 trigonometric functions are: Cosecant(csc), Secant(sec), and cotangent(cot)

10. M nemonics of SOHCAHTOA Trigonometric Ratios       The Reciprocal      

11. Example #1 What are the values of the 6 trigonometric ratios?            

12. Example #2 Opposite = α Hypotenuse = 13 θ = 23°       𝛼 = 5.08 units

13. Example #3 Opposite = 7 Adjacent = 24 θ = β    

14. Example #4

15. Example 5: A group of kids are playing basketball when the ball gets stuck between the hoop and the backboard, which is 3.2 meters high. One of the kids stands 4 meters away from the hoop and plans to throw a shoe to get the ball unstuck. Q. Determine the angle at which the kid should throw the shoe to hit the ball that is stuck.

16. Activity (by trio) On a one whole pad paper, copy and answer the following problem. Write the complete solution and illustration, then box the final answer. Problem #1: Find what is missing (x and θ) on the following illustrations, and complete the 6 trigonometric ratios: B. A.

17. Problem #2: A boy is standing on top of a building that is 65 feet tall. He throws a paper airplane, and it lands 112 feet away from the base of the building. A. What is the distance from the boy on top of the building to the point where the paper airplane lands? B. Determine the angle at which the boy released the paper airplane, relative to the building.