Lesson Plan Subject : Mathematics Level : F.4

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Presentation transcript:

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 : http://www.go.to/cwt

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

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

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

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

Simple trigonometric identities B A b c a Back to content

Simple trigonometric identities B A b c a Back to content

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Software related to the topic : Wingeom Quadrant.ge2 four quadrants Sin-cos.ge2 sine and cosine functions Tangent.ge2 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

Assignment ~ End ~ Textbook : Pleasurable Learning Mathematics Exercise 9A (P.81) Exercise 9B (P.84) Exercise 9C (P.86) Online Exercise : http://www.geocities.com/cwt_cwt/question-bank/f4_chapter9.htm ~ End ~ Back to content