mathematics. The modern and advanced meaning refers to the geometry of analytic varieties. This article focuses on the classical and elementary meaning. In classical mathematics‚ analytic geometry‚ also known as coordinate geometry‚ or Cartesian geometry‚ is the study of geometry using a coordinate system and the principles of algebra and analysis. This contrasts with the synthetic approach of Euclidean geometry‚ which treats certain geometric notions as primitive‚ and uses deductive reasoning based on axioms
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developed the coordinate system as a “device to locate points on a plane”. The coordinate system includes two perpendicular lines. These lines are called axes. The vertical axis is designated as y-axis while the horizontal axis is designated as the x-axis. The intersection point of the two axes is called the origin or point zero. The position of any point on the plane can be located by locating how far perpendicularly from each axis the point lays. The position of the point in the coordinate system is specified
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VCE Specialist Mathematics Pocket Study Guide Contents Introduction 1 Vectors in two and three dimensions 2 Complex numbers 3 Coordinate geometry and sketch graphs 4 Circular functions 5 Antidifferentiation 6 Integration 7 Differential equations 8 Kinematics 9 Vector calculus 10 Dynamics iv 1 12 26 40 53 62 70 79 86 92 Introduction What do you really need to know for Specialist Mathematics? We’ve answered that question in this Pocket Study Guide. This handy guide gives you a summary of
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René Descartes: "Father of Modern Mathematics" 1596-1650 December 13‚ 2004 René Descartes was born in La Haye‚ Touraine (France) in March of 1596 and died at Stockholm on February 11‚ 1650. René‚ the second of a family of two sons and one daughter‚ was sent to the Jesuit School at La Flêche at the early age of eight. Since he was of poor health he was permitted to lie in bed till late in the mornings‚ a custom which
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Course Code: Math 1 Course Title: College Algebra Year: 1st Year Topic: Functions Designer: Frago‚ Christine Joy S. Stage 1 – Desired Results Established Goals: This section aims to: 1. distinguish a function from a mere relation; and 2. find the domain and range of functions or relations Understandings: Students will understand… the definition of relation the definition of function the relationship between relation and function Essential Questions: Is the relation a function
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Chapter Objectives • Cartesian vector form • Dot product and angle between 2 vectors Copyright © 2010 Pearson Education South Asia Pte Ltd Chapter Outline 1. 2. 3. 4. 5. Cartesian Vectors Addition and Subtraction of Cartesian Vectors Position Vectors Force Vector Directed along a Line Dot Product Copyright © 2010 Pearson Education South Asia Pte Ltd 2.5 Cartesian Vectors • Right-Handed Coordinate System A rectangular or Cartesian coordinate system is said to be right-handed
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Cartesian Plane and Coordinate System Introduction: The Cartesian Plane consists of two perpendicular number lines. The vertical y-axis‚ and the horizontal x-axis. These two lines intersect at a point called the origin. This system establishes a correspondence between points in the plane and pairs of real numbers. For every pair of real numbers‚ there corresponds a point in the plane. The Cartesian Plane also consists of four quadrants. The top-right quarter is Quadrant I‚ the top-left is Quadrant
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“The Father of Modern Philosophy”‚ this title is supported by his contributions to philosophy and mathematics. The coordinate system‚ used today‚ is accredited to him along with many other mathematical contributions. He also had many contributions to philosophy‚ including his most famous‚ Meditations on First Philosophy. Every time you graph an equation on a Cartesian coordinate system‚ you are using the work of Rene Descartes. Born in La Haye on March 31‚ 1596‚ Descartes was sent to the Jesuit college
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Coordinate geometry The Basics: Find the distance between two points using Pythagoras’ theorem. The midpoint is the average (mean) of the coordinates. The gradient = Parallel lines have the same gradient. The gradients of perpendicular lines have a product of -1. Straight Lines: Equation of a straight line is y = mx + c‚ where m = gradient‚ c = y-intercept. The equation of a line‚ if we know one point and the gradient is found using: (y - y1) = m(x - x1) (If given two points‚ find the
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What is the reciprocal of the tangent function? Answer: Cotangent 5. What is the numbers used to locate a point in space? Answer: Coordinates 6. What is the point at which the axes of a coordinate system cross; the point (0‚0) in the Cartesian coordinate system? Answer: Origin 7. Any one of the four regions into which coordinates axis divide a plane. Answer: Quadrant 8. What is the quotient of two polynomials? Answer: Rational Expression 9. What is
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