GAUTENG DEPARTMENT OF EDUCATION SENIOR SECONDARY INTERVENTION PROGRAMME MATHEMATICS GRADE 12 SESSION 21 (LEARNER NOTES)

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1 MATHEMATICS GRADE SESSION (LEARNER NOTES) TRIGONOMETRY () Learner Noe: Trigonomery is an eremely imporan and large par of Paper. You mus ensure ha you maser all he basic rules and definiions, and be able o apply hese rules in many differen ypes of quesions. In his session you will be concenraing on Grade Trigonomery which involves compound and double angles. These Grade conceps will be inegraed wih he Trigonomery you sudied in Grade. Before aemping he ypical eam quesions, familiarise yourself wih he basics in Secion C. SECTION A: TYPICAL EXAM QUESTIONS Quesion ( minues) I is known ha sin 0 and an where [ 90 ; 70] and [90 ; 70 ]. 4 Deermine, wihou using a calculaor, he values of he following: (a) cos () (b) cos( ) (6) Quesion ( minues) If sin8 deermine he following in erms of. (a) cos8 (4) (b) sin78 () Page of 8

2 MATHEMATICS GRADE SESSION (LEARNER NOTES) SECTION B: SOLUTIONS AND HINTS (a) sin y r () () 44 α sin diagram Pyhagoras cos () cos (b) an 4 y 4 r cos( ) cos.cos sin.sin β diagram Pyhagoras r cos.cos sin.sin (6) Page of 8

3 MATHEMATICS GRADE SESSION (LEARNER NOTES) (a) sin8 8 r y diagram Pyhagoras cos8 (4) (b) cos8 sin 78 sin 60 8 sin 60.cos8 cos 60.sin8.. sin 608 sin60.cos8 cos60.sin8 and and () Page of 8

4 MATHEMATICS GRADE SESSION (LEARNER NOTES) SECTION C: ADDITIONAL CONTENT NOTES Summary of all Trigonomeric Theory sin y cos an y r r sin cos an sin cos an ( ; y) sin cos an sin cos an Reducion rules sin(80 ) sin sin(80 ) sin sin(60 ) sin cos(80 ) cos cos(80 ) cos cos(60 ) cos an(80 ) an an(80 ) an an(60 ) an sin(90 ) cos sin(90 ) cos cos(90 ) sin cos(90 ) sin sin( ) sin cos( ) cos an( ) an Whenever he angle is greaer han 60, keep subracing 60 from he angle unil you ge an angle in he inerval 0 ;60. Page 4 of 8

5 MATHEMATICS GRADE SESSION (LEARNER NOTES) Ideniies sin cos sin an cos Special angles Triangle A Triangle B From Triangle A we have: From Triangle B we have: sin 4 sin0 and sin 60 cos4 an 4 cos0 and an0 and cos60 an 60 For he angles 0 ; 90 ;80 ;70 ;60 he diagram below can be used. 90 y A(0 ;) B(; ) G( ; 0) 80 r C( ; ) D( ;) E( ; 0) 0 60 F(0 ; ) 70 Page of 8

6 MATHEMATICS GRADE SESSION (LEARNER NOTES) The following ideniies are imporan for ackling Grade Trigonomery: Compound angle ideniies sin(a B) sin A cos B cos Asin B sin(a B) sin A cos B cos Asin B cos(a B) cos A cos B sin Asin B cos(a B) cos A cos B sin Asin B Double angle ideniies cos sin cos sin sin cos cos sin cos cos sin SECTION D: HOMEWORK Quesion If cos p where p < 0 and [80 ; 60 ], deermine, using a diagram, an epression in erms of p for: (a) an (4) (b) cos () Quesion If sin6 a, deermine he value of he following in erms of a: cos7 cos sin7 sin (6) Page 6 of 8

7 MATHEMATICS GRADE SESSION (LEARNER NOTES) SECTION E: SOLUTIONS TO SESSION 0 HOMEWORK (a) sin 4 sin ( ) sin.cos sin.cos sin 4sin.cos 8sin.cos (b)() (an )( cos ).cos cos cos sin cos cos ( cos ) cos (cos ) (.cos cos ) (.cos ) (b)() cos cos cos cos cos cos sin cos cos sin (a) sin(4 ) sin 4.cos cos 4.sin.cos.sin cos sin cos sin sin.cos sin.cos sin 4sin.cos 8sin.cos cos cos cos cos cos ( cos ) (4) (.cos cos ) (.cos ) (6) cos cos cos cos sin4.cos cos4.sin.cos.sin cos sin () () Page 7 of 8

8 MATHEMATICS GRADE SESSION (LEARNER NOTES) (b) sin sin 4 sin.cos sin 4 cos sin sin.cos cos sin sin.cos 4 sin.cos cos sin sin.cos cos sin cos sin cos sin sin.cos cos sin cos sin cos sin cos sin cos sin (6) The SSIP is suppored by Page 8 of 8