Everything Maths Grade 12

10.2 CHAPTER 10. TRIGONOMETRY Derivation ofsin(α−β) EMCCH We can use sin(α +β) = sinα cosβ + cosα sinβ to show that sin(α−β) = s ...

CHAPTER 10. TRIGONOMETRY 10.2 we have that cos(α−β) = sin(90− (α−β)) = sin((90−α) +β)) = sin(90−α) cosβ + cos(90−α) sinβ = cosα ...

10.2 CHAPTER 10. TRIGONOMETRY Problem-solving Strategyfor Identities EMCCM The most important thing to remember when asked to pr ...

CHAPTER 10. TRIGONOMETRY 10.2 Example 2: Trigonometric Identities 2 QUESTION Deduce a formula for tan(α +β) in terms of tanα and ...

10.2 CHAPTER 10. TRIGONOMETRY is undefined for some angles θ. Thus the identity is also undefined for these θ, and hence is not ...

CHAPTER 10. TRIGONOMETRY 10.3 1 − siny− (1− 2 sin^2 y) 2 siny cosy− cosy =− 1 =⇒ 2 sin^2 y− siny cosy(2 siny− 1) =− 1 =⇒ siny(2 ...

10.3 CHAPTER 10. TRIGONOMETRY � � � � � A C B D O θ x x SOLUTION Step 1 : Identify a strategy We want CB, and we have CD and BD. ...

CHAPTER 10. TRIGONOMETRY 10.3 (a) Find AOCˆ in terms of θ. (b) Find an expression for: i. cosθ ii. sinθ iii. sin 2θ (c) Using th ...

10.3 CHAPTER 10. TRIGONOMETRY Problems in 3 Dimensions EMCCP Example 6: Height of tower QUESTION � � � � D h A B C b θ β α D is ...

CHAPTER 10. TRIGONOMETRY 10.3 Step 1 : Identify a strategy We have that the triangle ABD is right-angled. Thus we can relate the ...

10.4 CHAPTER 10. TRIGONOMETRY C B A D � � � � θ α x x Find the height of thetower BC in terms of x, tanθ and cos 2α. Find BC if ...

CHAPTER 10. TRIGONOMETRY 10.4 For example, the Manhattan distance between the point P 1 with coordinates (x 1 ;y 1 ) and the poi ...

10.4 CHAPTER 10. TRIGONOMETRY Summary of the Trigonometric Rules and Identities EMCCT Pythagorean Identity Cofunction Identities ...

CHAPTER 10. TRIGONOMETRY 10.4 (b) 3 sinθ = 2 cos^2 θ Prove the following identities (a) sin^3 θ =3sin θ− 4 sin3θ (b) cos^2 α(1− ...

Statistics 11 11.1 Introduction EMCCU In this chapter, you willuse the mean, median, mode and standard deviation of a set of dat ...

CHAPTER 11. STATISTICS 11.2 ̄−x 3 σ ̄−x 2 σ ̄x−σ ̄x ̄+x σ ̄+2x σ ̄+3x σ 68% 95% 99% What happens if the testwas very easy or ver ...

11.3 CHAPTER 11. STATISTICS (c) What mark must oneobtain in order to be inthe top 2% of the class? (d) Approximately 84% of the ...

CHAPTER 11. STATISTICS 11.4 So how does one ensure that ones sample isrepresentative? There are a variety of methodsavail- able, ...

11.4 CHAPTER 11. STATISTICS out exactly which function best fits a given set of data. We can find outthe equation of the regress ...

CHAPTER 11. STATISTICS 11.4 SOLUTION Step 1 : Drawing the graph The first step is to drawthe graph. This is shownbelow. 0 1 2 3 ...