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...

...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...

...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...

...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...

...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...

... 2. Quadrilateral
3. Pentagon
4. Hexagon
5. Heptagon
6. Octagon
7. Nonagon
8. Decagon
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...

...is not a problem!
Geometry (Ancient Greek: γεωμετρία; geo- "earth", -metri "measurement") "Earth-measuring" is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. Geometry is one of the oldest mathematical sciences. Initially a body of practical knowledge concerning lengths, areas, and volumes, in the 3rd century BC geometry was put into an axiomatic form by Euclid, whose...

...“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...

1183 Words |
3 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"},"analytics":{"googleId":"UA-32718321-1"}}