G9 Trigonometry.pdf

History of Trigonometry

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TRIGONOMETRY  Branch of ___________  Properties and applications of ratios associated with ______  Was developed after ________, _______, and ________.

TRIGONOMETRY  Greek words: “______” – triangle and “_______” – to measure  Literally means

 Was first applied in surveying, navigation, and _________

TRIGONOMETRY  Two Main Branches  _________________ – 2D or triangles in a plane  ___________________ – related to sides and angles of a spherical triangle

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ORIGIN OF TRIGONOMETRY  _______ – studied heavenly bodies (astronomy)  Celestial sphere – surface through which _______ seemed to move in an irregular way (1st observation)

Mathematicians who conributed in Trigonometry (Your Face Sounds Familiar)

HIPPARCHUS of Nicaea (c. 140 B.C.)  Mathematician and astronomer  Founder of trigonometry  Constructed the first accurate table of ratios of sides of a ____________

MENELAUS of Alexandria

(c. 100 B.C.)

 made significant contributions to _______________

Claude Ptolemy (c. 140 B.C.)

 Constructed a table of trigonometric ratios for angles between 0° and 180°  __________ – his work of art about trigonometry and astronomy

ORIGINS OF TRIGONOMETRY  ________ – no significant learning in trigonometry took place – the study of trigonometry was passed to _______ and _______

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ORIGINS OF TRIGONOMETRY  ___________ – knowledge of trigonometry was transferred back to Europe – revival of trigonometry was spearheaded by and (his ________)

ORIGINS OF TRIGONOMETRY  Trigonometry was discussed in connection with astronomy for a long period of time

Nasir Eddin (1201 - 1274)

 An Arab astronomer who first wrote about the treatise on trigonometry independent to __________

Bartholomaeus Pitiscus (1600s)

 A professor at University of Heidelberg wrote the first textbook which bear the title “______________” (first used of the word)

William Oughtred (1574 - 1660)

 Introduced the multiplication sign (x) and the abbreviation sin, cos, and tan

Basic Concepts in Geometry and Algebra

Review of Basic Concepts in Geometry and Algebra  Locates a position in a plane  Has no dimension  Denoted with a Capital Letter

Review of Basic Concepts in Geometry and Algebra  Part of a Line  Has a definite length

Review of Basic Concepts in Geometry and Algebra  Has infinite length but has no width and thickness  Has no endpoints

Review of Basic Concepts in Geometry and Algebra  Has length and width but has no thickness

Review of Basic Concepts in Geometry and Algebra  A line segment indicated by a direction through an arrowhead

Review of Basic Concepts in Geometry and Algebra  A geometric figure formed when two line segments (or rays) meet at a common point

Review of Basic Concepts in Geometry and Algebra 1) An angle less than 90° 2) An angle between 90° and 180° 3) A 90° angle 4) A 180° angle 5) ∠A and ∠B such that A + B = 180°

Review of Basic Concepts in Geometry and Algebra 6) ∠X and ∠Y such that X + Y = 90° 7) A triangle with a 90° angle 8) A triangle having two equal sides 9) A triangle with three equal sides

Review of Basic Concepts in Geometry and Algebra 10) A triangle with three equal angles 11) A right triangle with two equal sides 12) The square of the hypotenuse equals the sum of the square of the legs

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