522092120-The-Six-Trigonometric-Ratios-ppt.pptx

The-Six-Trigonometric-Ratios

1. MATHEMATICS 9 Demonstration Teaching Prepared by: Mary Joy B. Morada Teacher I

2. Checking of Attendance Name any tallest building around the world once your name is being called.

3. Review of the past lesson!

4. Review of the past lesson!

5. The Six Tigonometric Ratios Sine, Cosine, Tangent, Secant, Cosecant & Cotangent

6. I. OBJECTIVES At the end of the lesson, learners are expected to : 1. Illustrate the six trigonometric ratios: sine, cosine, tangent, secant, cosecant, and cotangent; 2. Find the value of the six trigonometric ratios from the given triangle; and 3. Appreciate the importance of trigonometry in real life situations.

7. TRIGONOMETRY 1. It is the branch of mathematics that deals with the relation between the sides and angles of a triangle . 2. From the Greek words “ trigonon ” trigon meaning triangle and “ metron ”, to measure. It is literally means “ measurement of triangles ”. 3. It is a tool used for measuring distances that cannot be directly measured . 4. Trigonometry involves the study of angles and geometric ratios.

8. 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. 1. Hypotenuse – is always the side opposite the right angle, it is the longest side of a right triangle. b Hypotenuse 2 . Opposite side – The side opposite the given acute angle. c Opposite 3 . Adjacent side – the side which is also a side of the given acute angle. a Adjacent side a c b

9. O J Y j o y Hypotenuse Opposite Adjacent side The Six Trigonometric Ratios Trigonometric Ratio Abbreviation Ratio of Lengths Sine of theta sin θ cosine of theta cos θ Tangent of theta tan θ Cosecant of theta csc θ secant of theta cos θ cotangent of theta cot θ Trigonometric Ratio Abbreviation Ratio of Lengths Sine of theta sin θ cosine of theta cos θ Tangent of theta tan θ Cosecant of theta csc θ secant of theta cos θ cotangent of theta cot θ SOH – CAH - TOA SOH = Sin (Opposite , hypotenuse) CAH = Cos (Adjacent , hypotenuse) TOA = Tan (Opposite, Adjacent )

10. Example: Find the value of the six trigonometric ratios of each of the acute angle of the given triangle C A R 8 24 16 sin A cos A tan A Hypotenuse Opposite Adjacent θ     csc A sec A cot A                                   CAR

11. Example: Find the value of the six trigonometric ratios of each of the acute angle of the given triangle C A R 8 24 16 sin C cos C tan C Hypotenuse Opposite Adjacent θ     csc C sec C cot C                               CAR  

12. Find the value of the six trigonometric ratios from the given triangle. See page 11 on your learner’s module Activity

13. Quiz I. Complete the sentence: In a right triangle having an acute angle, a. the sine θ is the ratio between _________and ___________. b. the cosine θ is the ratio between ___________ and ___________. c. the tangent θ is the ratio between __________and ____________.

14. Quiz I. Find the value of the six trigonometric ratios from the given triangle.

15. Quiz I. Find the value of the six trigonometric ratios from the given triangle.

16. Answer I. Complete the sentence: In a right triangle having an acute angle, a. the sine θ is the ratio between _________and ___________. b. the cosine θ is the ratio between ___________ and ___________. c. the tangent θ is the ratio between __________and ____________. Opposite Hypotenuse Adjacent Hypotenuse Opposite Adjacent

17. Quiz I. Find the value of the six trigonometric ratios from the given triangle.     Hypotenuse Opposite Adjacent        

18. Quiz I. Find the value of the six trigonometric ratios from the given triangle. Hypotenuse Opposite Adjacent            

19. Generalization Why d o you think Trigonometry is important in our life? Give some example

20. TRIGONOMETRY 1. It is the branch of mathematics that deals with the relation between the sides and angles of a triangle . 2. From the Greek words “ trigonon ” trigon meaning triangle and “ metron ”, to measure. It is literally means “ measurement of triangles ”. 3. It is a tool used for measuring distances that cannot be directly measured . 4. Trigonometry involves the study of angles and geometric ratios.

21. O J Y j o y Hypotenuse Opposite Adjacent side The Six Trigonometric Ratios Trigonometric Ratio Abbreviation Ratio of Lengths Sine of theta sin θ cosine of theta cos θ Tangent of theta tan θ Cosecant of theta csc θ secant of theta cos θ cotangent of theta cot θ Trigonometric Ratio Abbreviation Ratio of Lengths Sine of theta sin θ cosine of theta cos θ Tangent of theta tan θ Cosecant of theta csc θ secant of theta cos θ cotangent of theta cot θ SOH – CAH - TOA SOH = Sin (Opposite , hypotenuse) CAH = Cos (Adjacent , hypotenuse) TOA = Tan (Opposite, Adjacent )

22. Assignment Answer the activity page 15 in your module using calculator to find the Trigonometric Ratios.