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Lesson Plan Subject : Mathematics Level : F.4

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Presentation on theme: "Lesson Plan Subject : Mathematics Level : F.4"— Presentation transcript:

1 Lesson Plan Subject : Mathematics Level : F.4
Topic : Trigonometric Ratios Prepared by : CWT Textbook : Pleasurable Learning Mathematics Chapter 9 ( Section 9.1 to 9.4) Reference web-site :

2 Content Trigonometric ratios in right-angled triangle
Simple trigonometric identities Four quadrants Unit circle Signs of trigonometric ratios Trigonometric ratios of any angle Trigonometric ratios of special angle Software related to the topic

3 Trigonometric ratios in a right-angled triangle
opposite side C B A b c a Adjacent side hypotenuse Back to content

4 Trigonometric ratios in a right-angled triangle
opposite side C B A b c a Adjacent side hypotenuse Back to content

5 Trigonometric ratios in a right-angled triangle
opposite side C B A b c a Adjacent side hypotenuse Back to content

6 Simple trigonometric identities
B A b c a Back to content

7 Simple trigonometric identities
B A b c a Back to content

8 Simple trigonometric identities
B c a A C b Back to content

9 Simple trigonometric identities
B c a A C b Back to content

10 Simple trigonometric identities
B c a A C b Back to content

11 Quadrant Quadrant Quadrant Quadrant Quadrant II I III IV
o Quadrant 90 Quadrant II Quadrant I o o 180 o 0 or 360 Quadrant III Quadrant IV Back to content o o 270 or - 90

12 Unit Circle Back to content 90 y x 180 0 or 360 270 or - 90 ( x , y )
( 0 , 1 ) P ( x , y ) 1 y o x o o 180 x 0 or 360 C ( -1 , 0 ) O M A ( 1 , 0 ) D ( 0 , -1) Back to content o o 270 or - 90

13 In Quadrant I Back to content 90 y x 180 270 ( x , y ) y x o B
( 0 , 1 ) P ( x , y ) 1 y o o x 180 x C ( -1 , 0 ) O M A ( 1 , 0 ) D ( 0 , -1 ) Back to content o 270

14 In Quadrant I Back to content 90 y x 180 270 ( x , y ) y x o B
( 0 , 1 ) P ( x , y ) 1 y o x o 180 x C ( -1 , 0 ) O M A ( 1 , 0 ) D ( 0 , -1 ) Back to content o 270

15 In Quadrant I Back to content 90 y x 180 270 ( x , y ) y x o B
( 0 , 1 ) P ( x , y ) 1 y o x o 180 x C ( -1 , 0 ) O M A ( 1 , 0 ) D ( 0 , -1 ) Back to content o 270

16 In Quadrant II Back to content 90 y x 180 270 ( x , y ) y x o B
( 0 , 1 ) P ( x , y ) 1 y o x o 180 x C ( -1 , 0 ) O M A ( 1 , 0 ) D ( 0 , -1 ) Back to content o 270

17 In Quadrant II Back to content 90 y x 180 270 ( x , y ) y x o B
( 0 , 1 ) P ( x , y ) 1 y o x o 180 x C ( -1 , 0 ) O M A ( 1 , 0 ) D ( 0 , -1 ) Back to content o 270

18 In Quadrant II Back to content 90 y x 180 270 ( x , y ) y x o B
( 0 , 1 ) P ( x , y ) 1 y o x o 180 x C ( -1 , 0 ) O M A ( 1 , 0 ) D ( 0 , -1 ) Back to content o 270

19 In Quadrant III Back to content 90 y x 180 270 x y ( x , y ) o B
( 0 , 1 ) M x o x 180 o C ( -1 , 0 ) O A ( 1 , 0 ) y 1 P ( x , y ) D ( 0 , -1 ) Back to content o 270

20 In Quadrant III Back to content 90 y x 180 270 x y ( x , y ) o B
( 0 , 1 ) M x o x 180 o C ( -1 , 0 ) O A ( 1 , 0 ) y 1 P ( x , y ) D ( 0 , -1 ) Back to content o 270

21 In Quadrant III Back to content 90 y x 180 270 x y ( x , y ) o B
( 0 , 1 ) M x o x 180 o C ( -1 , 0 ) O A ( 1 , 0 ) y 1 P ( x , y ) D ( 0 , -1 ) Back to content o 270

22 In Quadrant IV Back to content 90 y x 180 270 x y ( x , y ) o B
( 0 , 1 ) x M o O x 180 o C ( -1 , 0 ) A ( 1 , 0 ) y 1 P ( x , y ) D ( 0 , -1 ) Back to content o 270

23 In Quadrant IV Back to content 90 y x 180 270 x y ( x , y ) o B
( 0 , 1 ) x M o O x 180 o C ( -1 , 0 ) A ( 1 , 0 ) y 1 P ( x , y ) D ( 0 , -1 ) Back to content o 270

24 In Quadrant IV Back to content 90 y x 180 270 x y ( x , y ) o B
( 0 , 1 ) x M o O x 180 o C ( -1 , 0 ) A ( 1 , 0 ) y 1 P ( x , y ) D ( 0 , -1 ) Back to content o 270

25 Summary Quadrant II Quadrant I Quadrant III Quadrant IV Sine All
o Summary 90 Quadrant II Sine Quadrant I All o 0 or 360 o 180 Quadrant III Tangent Quadrant IV Cosine Back to content o o 270 or - 90

26 Trigonometric ratios of any angle
90 y B ( 0 , 1 ) P ( x , y ) 1 y y o x o o 180 -x x 0 or 360 C ( -1 , 0 ) O M A ( 1 , 0 ) D ( 0 , -1) Back to content o o 270 or - 90

27 Trigonometric ratios of any angle
90 y B ( 0 , 1 ) P ( x , y ) 1 y y o 180 x o o -x x 0 or 360 C ( -1 , 0 ) O M A ( 1 , 0 ) D ( 0 , -1) Back to content o o 270 or - 90

28 Trigonometric ratios of any angle
90 y B ( 0 , 1 ) P ( x , y ) 1 y y o 180 x o o -x x 0 or 360 C ( -1 , 0 ) O M A ( 1 , 0 ) D ( 0 , -1) Back to content o o 270 or - 90

29 Trigonometric ratios of any angle
90 y B ( 0 , 1 ) P ( x , y ) 1 y o -x 180 x o o x 0 or 360 C ( -1 , 0 ) O M A ( 1 , 0 ) -y D ( 0 , -1 ) Back to content o o 270 or - 90

30 Trigonometric ratios of any angle
90 y B ( 0 , 1 ) P ( x , y ) 1 y o -x 180 x o o x 0 or 360 C ( -1 , 0 ) O M A ( 1 , 0 ) -y D ( 0 , -1) Back to content o o 270 or - 90

31 Trigonometric ratios of any angle
90 y B ( 0 , 1 ) P ( x , y ) 1 y o -x 180 x o o x 0 or 360 C ( -1 , 0 ) O M A ( 1 , 0 ) -y D ( 0 , -1) Back to content o o 270 or - 90

32 Trigonometric ratios of any angle
90 y B ( 0 , 1 ) P ( x , y ) 1 y o o o 180 x x 0 or 360 C ( -1 , 0 ) O M A ( 1 , 0 ) -y D ( 0 , -1) Back to content o o 270 or - 90

33 Trigonometric ratios of any angle
90 y B ( 0 , 1 ) P ( x , y ) 1 y o o o 180 x x 0 or 360 C ( -1 , 0 ) O M A ( 1 , 0 ) -y D ( 0 , -1) Back to content o o 270 or - 90

34 Trigonometric ratios of any angle
90 y B ( 0 , 1 ) P ( x , y ) 1 y o o o 180 x x 0 or 360 C ( -1 , 0 ) O M A ( 1 , 0 ) -y D ( 0 , -1) Back to content o o 270 or - 90

35 o Summary 90 o 0 or 360 o 180 Back to content o o 270 or - 90

36 Trigonometric ratios of special angle 45o
x 1 1 Back to content

37 Trigonometric ratios of special angle 30o ,60o.
2 2 y 1 1 Back to content

38 Trigonometric ratios of special angle 0o , 90o , 180o , 270o , 360o.
sin 0o = 0 cos 0o = 1 tan 0o = 0 sin 270o = -1 cos 270o = 0 tan 270o = u O M P ( x , y ) 1 x y ( 0 , 1 ) sin 90o = 1 cos 90o = 0 tan 90o = u sin 360o = 0 cos 360o = 1 tan 360o = 0 ( - 1 , 0 ) ( 1 , 0 ) sin 180o = 0 cos 180o = -1 tan 180o = 0 ( 0 , - 1 ) where u stand for undefined Back to content

39 Software related to the topic : Wingeom
Quadrant.ge2 four quadrants Sin-cos.ge sine and cosine functions Tangent.ge tangent function Trigo.ge2 Note : the wingeom file cannot be opened automatically by clicking the hyperlink, it only goes to the wingeom program, you have to click 2-dim, file, old..., and then choose the corresponding file. Back to content

40 Assignment ~ End ~ Textbook : Pleasurable Learning Mathematics
Exercise 9A (P.81) Exercise 9B (P.84) Exercise 9C (P.86) Online Exercise : ~ End ~ Back to content


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