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Understanding Quadrilaterals and Trigonometric Functions in Geometry

This document explores geometric concepts involving quadrilateral ABCD in the coordinate plane, focusing on points E, F, and G, and calculating the length of AG. It also humorously touches on an incident involving a math teacher at JFK Airport and highlights the importance of mathematical tools in teaching. Additionally, it covers trigonometric functions, their inverses, and practical applications using graphing calculators. Students are prompted to engage with various exercises to deepen their understanding of angles and trigonometric identities.

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Understanding Quadrilaterals and Trigonometric Functions in Geometry

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  1. Flashback 9-26-12 • Quadrilateral ABCD is drawn on the standard (x,y) coordinate plane as shown below, with points E and F on AD. Point G is the center of rectangle BCEF. How many coordinate units long is AG? • A. • B. • C. • D. • E.11

  2. Joke of the day You hear a news report on TV, and it says…At John F. Kennedy International Airport today, a Caucasian male (later discovered to be a high school mathematics teacher) was arrested trying to board a flight while in possession of a compass, a protractor and a graphical calculator.

  3. According to law enforcement officials, he is believed to have ties to the Al-Gebra network. He will be charged with carrying weapons of math instruction.

  4. Do trig functions have inverses? • Only if we restrict the domains

  5. Using inverses to find angles • Cos -1 (-0.5) • Sin x = 0.7 in 0 < x < 2∏

  6. Practical application • Enter data on p. 49 into L1 and L2 on your calculator. • Calculate sinreg

  7. homework • P. 53 #24, 27- 30, 31,32,35 • By Friday, p. 55 Quick Quiz 1-4. Must show work to get any credit.

  8. Exit Slip • True or false: The period of y = sin(x/2) is ∏. Justify your answer.

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