CHAPTER 15 TRIGONOMETRIC WAVEFORMS
EXERCISE 68 Page 163
1. Find all the angles between 0 and 360 whose sine is 0.7321
Sine is negative in the 3rd and 4th quadrants.
sin 1 (0.7321)
= 47.06 as shown in the diagram below.
From the diagram, the two angles bet
CHAPTER 17 TRIGONOMETRIC IDENTITIES AND EQUATIONS
EXERCISE 76 Page 190
1. Prove the identity: sin x cot x = cos x
L.H.S. = sin x cot x = sin x
2. Prove the identity:
1
cos x
sin x
tan x
sin x
= cosec
1
= cos x = R.H.S.
(1 cos 2 )
L.H.S. =
1
1 cos
2
CHAPTER 14 THE CIRCLE AND ITS PROPERTIES
EXERCISE 62 Page 148
1. If the radius of a circle is 41.3 mm, calculate the circumference of the circle
Circumference, c = 2r = 2(41.3) = 259.5 mm
2. Find the diameter of a circle whose perimeter is 149.8 cm
If per
CHAPTER 13 CARTESIAN AND POLAR CO-ORDINATES
EXERCISE 60 Page 144
1. Express (3, 5) as polar co-ordinates, correct to 2 decimal places, in both degrees and in radians.
From the diagram,
= 5.83
r 3 5
2
and
y
5
tan 1 tan 1
x
3
2
= 59.04 or
59.04
180
rad =
CHAPTER 9 SOLVING EQUATIONS BY ITERATIVE METHODS
EXERCISE 36 Page 83
1. Find the positive root of the equation x + 3x - 5 = 0, correct to 3 significant figures, using the
2
method of bisection.
Let f(x) =
x 3x 5
2
then, using functional notation:
f(0) = -
CHAPTER 6 ARITHMETIC AND GEOMETRIC PROGRESSIONS
EXERCISE 25 Page 52
1. Find the 11th term of the series 8, 14, 20, 26, .
The 11th term of the series 8, 14, 20, 26, is given by:
a + (n 1)d
where
a = 8, n = 11 and d = 6
Hence, the 11th term is: 8 + (11 1)(6
CHAPTER 1 ALGEBRA
EXERCISE 1 Page 4
1. Evaluate 2ab + 3bc - abc when a = 2, b = - 2 and c = 4
When a = 2, b = - 2 and c = 4, 2ab + 3bc - abc = 2(2)(- 2) + 3(- 2)(4) (2)(- 2)(4)
= - 8 24 + 16 = - 16
2. Find the value of 5pq r when p =
2
When p =
2
5
3
, q
EXERCISES PDE 31.10.12-02.11.12
1. Exercise
Let U R be a bounded open set. We say that v C 2 (U ) is subharmonic i v 0 in U .
(a) Prove that subharmonic functions enjoy the following form of the mean-value property: for
every x U , for every r > 0 such th
S CHOOL OF RANDOM DEPARTMENT NAMES
This is the title of the project report
Firstname Lastname
March 15, 2011
1 H EADING ON LEVEL 1 ( SECTION )
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mcode.sty Demo
Florian Knorn, florian@knorn.org
April 16, 2014
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