1 (a)Show that = tan θ.
(b)Hence find the value of cot in the form a + , where a, b .
2 If x satisfies the equation , show that 11 tan x = a + b, where a, b +.

3 The graph below shows y = a cos (bx) + c.

Find the value of a, the value of b and the value of c.

4 The diagram below shows two concentric circles with centre O and radii 2 cm and 4 cm. The points P and Q lie on the larger circle and angle POQ = x, where 0 < x < π2.

Show that the area of the shaded region is 8 sin x – 2x.

6 In the diagram below, AD is perpendicular to BC.
CD = 4, BD = 2 and AD = 3. = and = .

Find the exact value of cos ( − ).

8 Let sin x = s.
(a)Show that the equation 4 cos 2x + 3 sin x cosec3 x + 6 = 0 can be expressed as 8s4 – 10s2 + 3 = 0.
(b)Hence solve the equation for x, in the interval [0, π].

9 A particle P moves in a straight line with displacement relative to origin given by
s = 2 sin (πt) + sin(2πt), t ≥ 0,
where t is the time in seconds and the displacement is measured in centimetres. (i) Write down the period of the function s.

10 The diagram below shows a curve with equation y = 1 + k sin x, defined for 0 ≤ x ≤ 3π.
The point A lies on the curve and B(a, b) is the maximum point.
(a)Show that k = –6.
(b)Hence, find the values of a and b.

11 The depth, h (t) metres, of water at the entrance to a harbour at t hours after midnight on a particular day is given by
h (t) = 8 + 4 sin...

...The Matrix and Philosophy
Have you ever felt like the life you are living right now is not real? You do
not know what is real and what is not real? You doubt your very existence. These
were main problems for Neo, the main character of the movie “The Matrix”. Neo
thought he was living a normal life, but he felt like something was wrong, he did
not know what it was, could not explain it, but something was wrong. Later on
Neo learns the truth from a man named Morpheus; he found out that what he
thought was real was actually not real at all, it was all a computer program. The
life he lived was all a lie because of his perception blocking out reality. “The
Matrix” can be compared to ontology, the study of being or what is, “The Matrix”
relates to both dualism, both body and mind are affected, and finally it relates to
the brain in a vat and the “evil genius” ruining his view of life.
Parmenides was a philosopher who believed that all reality is one, it is not a
plurality, and reality is being. He came up with “Ontology” or in Greek
“Ontos”, ontology is the study of being or “what is”. Ontology has two parts to it
one, what is, is and two, what is not is not, which is not being. The universe
consists of one thing, it never changes, it has no parts, and it can never be
destroyed, all this being one. Ontology is metaphysics. “Physics is concerned with
the microscopic processes that underlie macroscopic reality; metaphysics is
concerned with...

...Collaboration Component Form
Please complete this four-part guide, and
submit for the collaboration component.
Make sure to save this file with the module number (no periods)
and your name. Thank you.
1. Collaboration lesson/task description: Describe the lesson or task you completed collaboratively
in a paragraph consisting of five or more sentences.
or more sentence , tons of details, excellent grammar, punctuation and spelling
2. Peer and self-evaluation: Rate each member of the team, including yourself, according to each of
the performance criterion below.
3 = above average
2 = average
1 = below average
f you attended a live
Listened to others
Showed respect for others' opinions
Completed assigned duties
Participated in discussions
Attended meetings
Stayed on task
Offered relevant information
Completed work adequately
Completed work on time (with no
reminders)
Offered appropriate feedback when
necessary
Created on Friday, November 22, 2013
Name of
Student 8
Name of
Student 7
Name of
Student 6
Name of
Student 5
Name of
Student 4
Name of
Student 3
Name of
Student 2
Your name
Category
.
3. Self-reflection: Respond to the
to
spelling
:
sentences each, tons of details, excellent grammar, punctuation and
Explain what you enjoyed most about working with others on this lesson/task.
Explain how your team dealt with conflict.
Explain how you feel others felt about your...

...Geometry
Assignment
Date: 24 June 2013
A. Name each of the following. Refer to the figure below. Write your answer in a one whole sheet of paper.
1. a circle
2. three radii
3. a diameter
4. a tangent
5. a secant
6. three chords
7. point of tangency
8. central angle
9. four minor arcs
10. at least two major arcs
B. Indicate whether each statement is true or false.
1. All radii of a circle are congruent.
2. A radius is a chord of a circle.
3. A line may intersect a circle at exactly one point.
4. A circle and a line may have three points in common.
5. Every chord in a circle contains two points of the circle.
6. A chord is not a diameter.
7. A secant may contain a chord.
8. A secant may pass through the centre of a circle.
9. A tangent to a circle intersects a radius.
10. All radii have the same measure.
Activity Sheet
Directions: Help each person decide what to do by applying your knowledge on special products on each situation.
1. Jem Boy wants to make his 8 meters square pool into a rectangular one by increasing its length by 2 m and decreasing its width by 2 m. Jem Boy asked your expertise to help him decide on certain matters.
a. What will be the new dimensions of Jem Boy’s pool?
b. What will be the new area of Jem Boy’s pool? What special product will be use?
c. If the sides of the square pool is unknown, how will you represent its area?
d. If Jem Boy does not want the area of his pool to...

...Geometry was throughly organized in about 300 B.C, when the Greek mathematician, Euclid gathered what was known at the time; added original book of his ownand arranged 465 propositions into 13 books called Elements.
Geometry is the mathematics of space and shape, which is the basis of all things that exist. Understanding geometry is necessary step by understanding how the things in our world exist. The applications of geometry in real life are not always evident to teenagers, but the reality is geometry infiltratesevery facet of our daily living.
Geometry was recognized to be not just for mathematicians. Anyone can benefit from the basic learning of geometry, which is to follow the lines reasoning. Geometry is one of the oldest sciences and is corcerned with questions of shape, size and relative position of figures and with properties of space.
Geometry is considered an important field pf study because of its applications in daily life.
Geometry is mainly divided in to two which is plane geometry and solid geometry. Plane geometry is about all kinds of two dimensional shapes such as lines, circles, and triangles. While Solid geometry is about all kinds of three dimensional shapes like polygons, prisms, pyramids, sphere and cylinder.
Now, let’s move on its...

...Rashin-Coatie Analysis
Rashin-Coatie is a story about a gentleman and his two daughters in Scotland. One daughter is ugly, mean, and older and the other is very good looking, younger, and very nice. The parents hate the young good looking daughter, and love the ugly ill-natured daughter. The parents mistreat their young daughter making her do all of the hard work and give her very little food and water. The daughter has a calf that helps her get away from her parents and her bad sister. The parents try to kill the calf, instead the girl and the calf escape running to a meadow where she gets rashes from poison oak. She is now named Rashin-Coatie. The calf and the young daughter travel to the king’s house where they ask the king if he needs a servant. The mistress hires the young daughter as a kitchen servant. Everyone liked her. The calf gave her a dress and glass slippers to wear at the dinner and she impressed everyone, the prince fell in love with her. She left without meeting him, and lost one of her slippers. He looked all over for the girl who lost this slipper, having every woman in the town try on this slipper. The prince made a promise to marry the one who fit the shoe. The ugly daughter cut her foot to make the slipper fit and so the prince was tricked. He knew it was not the girl he was looking for, but he made a promise so he had to honor it. The prince was very angry. He was going to marry the ugly daughter, until a little bird flew in and told him to look...

...“Bringing it all Together: The Geometry of Golf”
Golf in Geometry?? No Way!
Geometry In The Game of Golf
For hundreds of years, golf has been an extremely popular and growing sport all around the world. Looking where golf is now, it is growing rapidly from the young to the elder population. The first round of gold was first played in the 15th century off the coast of Scotland, but it did not start to be played until around 1755. The standard rules of golf were written by a group of Edinburgh golfers. Today, people of the US, Scotland, and England, have been drawn to the game because it is fun, challenging, and hardly any athletic ability at all is required for amateurs. In breaking down the game, geometry plays a major role, and can influence a players score dramatically. Geometry plays a key role and influences aspects such as the ball, course, or golf swing.
First Geometry is important in the design of the golf ball. It is crucial that the golf ball is not a perfect sphere, but as close to a sphere as possible. Before man could create the perfect golf ball, the main idea was to create a close to perfect sphere without any implications that would mess up the distance and direction of the ball. If the ball is not a perfect sphere, without any davits, the ball would not get any spin on it and would go the wrong direction.
Furthermore geometry is used in...

... 9. Dodecagon
10. Tetradecagon
F. Circles
Introduction
"Geometry," meaning "measuring the earth," is the branch of math that has to do with spatial relationships. In other words, geometry is a type of math used to measure things that are impossible to measure with devices. For example, no one has been able take a tape measure around the earth, yet we are pretty confident that the circumference of the planet at the equator is 40,075.036 kilometres (24,901.473 miles) . How do we know that? The first known case of calculating the distance around the earth was done by Eratosthenes around 240 BCE. What tools do you think current scientists might use to measure the size of planets? The answer is geometry.
However, geometry is more than measuring the size of objects. If you were to ask someone who had taken geometry in high school what it is that s/he remembers, the answer would most likely be "proofs." (If you were to ask him/her what it is that s/he liked the least, the answer would probably be "proofs.") A study of Geometry does not have to include proofs. Proofs are not unique to Geometry. Proofs could have been done in Algebra or delayed until Calculus. The reason that High School Geometry almost always spends a lot of time with proofs is that the first great Geometry textbook, "The Elements," was written exclusively with proofs....

...of mathematics in combination with his artistic skill provides a rare translation between the seemingly separate languages of math and art. "In mathematical quarters, the regular division of the plane has been considered theoretically . . . Does this mean that it is an exclusively mathematical question? In my opinion, it does not. [Mathematicians] have opened the gate leading to an extensive domain, but they have not entered this domain themselves. By their very nature thay are more interested in the way in which the gate is opened than in the garden lying behind it." (M.C. Escher on tessellations viewed at Alhambra www.mathacedemy.com)
The variety of math used in his body work extends from basic geometric shape to hyperbolic geometry; though there is no need to cover such a wide subject range to explain mathematic influence. Escher was first inspired by the gridded tile patterns, designed in the 14th Century by the Moors, at the Alhambra castle in Granada. Escher was fascinated by the idea of dividing the plane with geometric shapes. Tassellations, the arrangement of closed shapes that do not overlap or allow gaps, became a staple in his work. Typically tassellations are created with regular shapes, such as polygons. Escher was inspired by these patterns and the richness they added to a two dimensional surface, though also understood the geometric concept of three dimensions. Escher was interested in translating the concepts, and line...