Everything Maths Grade 10

Step 3: Use your calculator to solve for To solve for , you will need to use the inverse cosine function on your calculator. Thi ...

5.8 Defining ratios in the Cartesian plane EMA3X We have defined the trigonometric ratios using right-angled triangles. We can e ...

Similarly, an alternative method is to calculate the hypotenuse using the theorem of Pythagoras and calculate using: sin = oppos ...

0 0 ◦ 360 ◦ 90 ◦ 180 ◦ 270 ◦ Quadrant II Quadrant I Quadrant III Quadrant IV A all ratios S sin T tan C cos This diagram is k ...

Therefore: sin 0 °= opposite hypotenuse = 0 hypotenuse = 0 cos 0 °= adjacent hypotenuse = hypotenuse hypotenuse = 1 tan 0 °= opp ...

Step 2: Use the theorem of Pythagoras to calculater r^2 =x^2 +y^2 = (3)^2 + (4)^2 = 25 )r= 5 Noteris positive as it is the radiu ...

Step 2: Use the theorem of Pythagoras to calculatey r^2 =x^2 +y^2 y^2 =r^2 x^2 = (13)^2 (5)^2 = 169 25 = 144 y=± 12 Given thatl ...

2.Ifsin=0,4 andis an obtuse angle, determine: a) cos b) p 21 tan 3.Giventan= t 2 , where 0 ° 90 °. Determine the followi ...

10.Iftan = 5 12 and 0 ◦  180 ◦, determinewithout the use of a calculatorthe value of 12 cos For more exercises, visit http:// ...

a) tan 80 ◦ b)cos 73 ◦ c) sin 17 ◦ d)tan 313 ◦ e) cos 138 ◦ f)sec 56 ◦ g) cot 18 ◦ h) cosec 37 ◦ i)sec 257 ◦ j)sec 304 ◦ k) 3 si ...

c)tan 60 ◦sin 60 ◦tan 60 ◦ p 3 2 p 3 1 1 2 1 1 1 p 2 d)sin 30 ◦sin 30 ◦sin 30 ◦ 1 2 1 2 p 3 1 8 1 4 p 3 4 p 2 e)sin 45 ◦ ...

9.A right-angled triangle has hypotenuse 13 mm. Find the length of the other two sides if one of the angles of the triangle is 5 ...

f) 9,k9 x◦ 6 g) (^7) 5,73 x◦ h) 2,54 x◦ 5,44 i) 7 40 ◦ x 11.Calculate the unknown lengths in the diagrams below: 30 ◦ 25 ◦ 20 ◦ ...

13.In the following triangle find the size ofABC^. 41 ◦ 9 A D C B 17 14.In the following triangle find the length of sideCD: A D ...

18.Ifa= 29°,b= 38°andc= 47°, use your calculator to evaluate each of the following, correct to 2 decimal places. a) tan(a+c) b)c ...

CHAPTER^6 Functions 6.1 Introduction 146 6.2 Linear functions 150 6.3 Quadratic functions 158 6.4 Hyperbolic functions 167 6.5 E ...

6 Functions 6.1 Introduction EMA3Z Functions are mathematical building blocks for designing machines, predicting natural disaste ...

Set notation EMA43 Examples: fx:x 2 R; x > 0 g The set of allx-values such thatxis an element of the set of real numbers and ...

1.Words: “The relationship between two variables is such that one is always 5 less than the other.” 2.Mapping diagram: 0 x 5 5 ...

c) x 2 8 10 12 y 1 2 3 6 4.Plot the following points on a graph. a) x 1 2 3 4 5 6 y 0,1 0,2 0,3 0,4 0,5 0,6 b) x 1 2 3 4 5 6 y 5 ...