Everything Maths Grade 11

CHAPTER 17. TRIGONOMETRY 17.3 Reduction Formula EMBDD Any trigonometric function whose argument is 90 ◦±θ; 180 ◦±θ; 270 ◦±θ and ...

17.3 CHAPTER 17. TRIGONOMETRY Activity: Reduction Formulae forFunction Values of 360 ◦±θ Function values of (360◦− θ) (a) In t ...

CHAPTER 17. TRIGONOMETRY 17.3 values are in fact equal: sin293◦ =− 0 , 92... −sin67◦ =− 0 , 92... Example 4: More Complicated QU ...

17.3 CHAPTER 17. TRIGONOMETRY (a) sin163◦ (b) cos327◦ (c) tan248◦ (d) cos213◦ Determine the following without the use of acalcu ...

CHAPTER 17. TRIGONOMETRY 17.3 (a) In the figure P and P�lie on the cir- cle with radius 2. OP makes an angle θ = 30◦with the x-a ...

17.3 CHAPTER 17. TRIGONOMETRY SOLUTION cos50◦= sin(90◦− 50 ◦) = sin40◦ sin320◦= sin(360◦− 40 ◦) =−sin40◦ cos230◦= cos(180◦+ 50◦ ...

CHAPTER 17. TRIGONOMETRY 17.4 17.4 Solving Trigonometric Equations EMBDE In Grade 10 and 11 wefocused on the solutionof algebrai ...

17.4 CHAPTER 17. TRIGONOMETRY Example 6: QUESTION Find θ, if tan θ + 0,5 = 1, 5 , with 0 ◦< θ < 90 ◦. Determine the soluti ...

CHAPTER 17. TRIGONOMETRY 17.4 is solved as sin θ = 0, 5 = 30◦ On your calculator youwould type sin−^1 ( 0 , 5 ) =to find the siz ...

17.4 CHAPTER 17. TRIGONOMETRY infinite number of solutions to this equation! This difficulty (which is caused by the periodicity ...

CHAPTER 17. TRIGONOMETRY 17.4 y x 1 − 1 360 − 180 − 180 360 Step 2 : Notice that this line touches the graph four times. This me ...

17.4 CHAPTER 17. TRIGONOMETRY 0 1 − 1 90 ◦◦ 180 270 ◦◦ 360 1 st 2 nd 3 rd 4 th +V E +V E−V E−V E 0 ◦/ 360 ◦ 90 ◦ 180 ◦ 270 ◦ 2 n ...

CHAPTER 17. TRIGONOMETRY 17.4 using the CAST diagram(Figure 17.13). This diagram is known as a CAST diagram as the letters, take ...

17.4 CHAPTER 17. TRIGONOMETRY Step 1 : Determine in which quadrants the solution lies We look at the sign ofthe trigonometric fu ...

CHAPTER 17. TRIGONOMETRY 17.4 This is the general solution. Notice that we added the 10 ◦and divided by 2 only at the end. Notic ...

17.4 CHAPTER 17. TRIGONOMETRY SOLUTION 3cos(θ− 15 ◦)− 1 =− 2 , 583 3cos(θ− 15 ◦) =− 1 , 583 cos(θ− 15 ◦) =− 0 , 5276... referenc ...

CHAPTER 17. TRIGONOMETRY 17.4 And then we are left with two linear trigonometric equations. Be careful: sometimes one of the two ...

17.4 CHAPTER 17. TRIGONOMETRY cos x =− 0 ,5 [60◦] II : x = 180◦− 60 ◦+ (360◦. n);n∈Z = 120◦+ (360◦. n);n∈Z III : x = 180◦+ 60◦(3 ...

CHAPTER 17. TRIGONOMETRY 17.4 Exercise 17 - 10 (a) Find the general solution of each of thefollowing equations. Give answers to ...

17.5 CHAPTER 17. TRIGONOMETRY 17.5 Sine and Cosine Identities EMBDM There are a few identities relating to the trigonometric fun ...