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 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...

...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...

...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...

... 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....

...Geometry Rationale
Geometry is Greek for geos, which means Earth, and metron meaning measure. It can conceivably lay claim to being the oldest branch of mathematics outside arithmetic, and humanity has probably used geometrical techniques since before the dawn of recorded history. Initially, as with the Egyptians, geometry originated from practical necessity and the need to measure land. Geometry today is the science of observing and measuring shapes, surfaces, angles, lines and the relationships between these things. One might think that Geometry is sort of removed from daily life, but we are constantly surrounded by it. Everything in our environment has shape, lines, surfaces and angles and so the child has been experiencing these things in everything that surrounds them.
"Pythagoras was a Greek who was born in Samos about 580 BC. When he was nearly fifty years old he went to live in Italy near the city of Naples. He founded a religious order, which meant that he spent much of his time walking about with other men like him in long robes and thinking about the divine order in the universe. Pythagoras and his friends were looking for harmony, which they found all about them. Pythagoras had studied music, especially the harp. He noted a relationship between the harmony in the music and the study of mathematics. Other people of that time thought they could find answers to their questions about the...

...Fractal Geometry
"Fractal Geometry is not just a chapter of mathematics, but one that helps
Everyman to see the same old world differently". - Benoit Mandelbrot
The world of mathematics usually tends to be thought of as abstract. Complex and
imaginary numbers, real numbers, logarithms, functions, some tangible and others
imperceivable. But these abstract numbers, simply symbols that conjure an image,
a quantity, in our mind, and complex equations, take on a new meaning with
fractals - a concrete one. Fractals go from being very simple equations on a
piece of paper to colorful, extraordinary images, and most of all, offer an
explanation to things. The importance of fractal geometry is that it provides an
answer, a comprehension, to nature, the world, and the universe. Fractals occur
in swirls of scum on the surface of moving water, the jagged edges of mountains,
ferns, tree trunks, and canyons. They can be used to model the growth of cities,
detail medical procedures and parts of the human body, create amazing computer
graphics, and compress digital images. Fractals are about us, and our existence,
and they are present in every mathematical law that governs the universe. Thus,
fractal geometry can be applied to a diverse palette of subjects in life, and
science - the physical, the abstract, and the natural.
We were all astounded by the sudden revelation that the output of a
very simple, two-line...

1529 Words |
5 Pages

Share this Document

{"hostname":"studymode.com","essaysImgCdnUrl":"\/\/images-study.netdna-ssl.com\/pi\/","useDefaultThumbs":true,"defaultThumbImgs":["\/\/stm-study.netdna-ssl.com\/stm\/images\/placeholders\/default_paper_1.png","\/\/stm-study.netdna-ssl.com\/stm\/images\/placeholders\/default_paper_2.png","\/\/stm-study.netdna-ssl.com\/stm\/images\/placeholders\/default_paper_3.png","\/\/stm-study.netdna-ssl.com\/stm\/images\/placeholders\/default_paper_4.png","\/\/stm-study.netdna-ssl.com\/stm\/images\/placeholders\/default_paper_5.png"],"thumb_default_size":"160x220","thumb_ac_size":"80x110","isPayOrJoin":false,"essayUpload":false,"site_id":1,"autoComplete":false,"isPremiumCountry":false,"userCountryCode":"US","logPixelPath":"\/\/www.smhpix.com\/pixel.gif","tracking_url":"\/\/www.smhpix.com\/pixel.gif","cookies":{"unlimitedBanner":"off"},"essay":{"essayId":37995166,"categoryName":"Literature","categoryParentId":null,"currentPage":1,"format":"text","pageMeta":{"text":{"startPage":1,"endPage":2,"pageRange":"1-2","totalPages":2}},"access":"premium","title":"Geometry and Sin","additionalIds":[19,9,108,219,13],"additional":["Natural Sciences","Entertainment","Entertainment\/Music","Natural Sciences\/Mathematics","Health \u0026 Medicine"],"loadedPages":{"html":[],"text":[1,2]}},"user":null,"canonicalUrl":"http:\/\/www.studymode.com\/essays\/Geometry-And-Sin-1735117.html","pagesPerLoad":50,"userType":"member_guest","ct":10,"ndocs":"1,500,000","pdocs":"6,000","cc":"10_PERCENT_1MO_AND_6MO","signUpUrl":"https:\/\/www.studymode.com\/signup\/","joinUrl":"https:\/\/www.studymode.com\/join","payPlanUrl":"\/checkout\/pay","upgradeUrl":"\/checkout\/upgrade","freeTrialUrl":"https:\/\/www.studymode.com\/signup\/?redirectUrl=https%3A%2F%2Fwww.studymode.com%2Fcheckout%2Fpay%2Ffree-trial\u0026bypassPaymentPage=1","showModal":"get-access","showModalUrl":"https:\/\/www.studymode.com\/signup\/?redirectUrl=https%3A%2F%2Fwww.studymode.com%2Fjoin","joinFreeUrl":"\/essays\/?newuser=1","siteId":1,"facebook":{"clientId":"306058689489023","version":"v2.8","language":"en_US"}}