By James Tanton
This advisor covers the tale of trigonometry. it's a speedy assessment, however it is entire within the context of the content material mentioned in starting and complicated high-school classes. the aim of those notes is to complement and positioned into viewpoint the cloth of any path at the topic you have taken or are at the moment taking. (These notes might be difficult going for these encountering trigonometry for the first actual time!)
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Additional resources for Trigonometry A Clever Study Guide
Sample text
1 Walking all the way round the circumference of this circle corresponds to walking a distance of 2π × 1 = 2π units. Thus it seems natural to associate the number 2π with the concept of one full turn, and fractions of this number with fractions of turns. For example, we associate the number 1 3 3 · 2π = π with half a turn and the number 10 · 2π = 3π with 10 of a turn. 2 5 These numbers are the distances one physically traverses when walking these fractions of a full turn on a circle of radius one unit.
2 x = −45◦ a –45 –a 1 Positive angles are measured counterclockwise from the positive x-axis, negative angles in a clockwise direction. 1 sin(−45◦ ) = − √ 2 1 cos(−45◦ ) = √ . 2 x = 60◦ 1 a 60 1 2 The Basics of “Circle-ometry” 1 . 2 25 We see half an equilateral triangle of side length 1. Thus cos(60◦ ) = (Ooh! ) The Pythagorean Theorem gives a= 1− 1 2 2 = √ 3 2 and so sin (60◦ ) = √ 3 . 866 2 1 cos (60◦ ) = . 2 sin (60◦ ) = x = 30◦ 1 2 1 30 a Again we have half an equilateral triangle. sin (30◦ ) = cos (30◦ ) = 1 2 √ 3 .
What is the length of its hypotenuse? (A) 57 4 (B) 59 4 (C) 61 4 (D) 63 4 (E) 65 4 5. (#11, AMC 10A, 2011) Square E F G H has one vertex on each side of square ABC D. Point E is on AB with AE = 7 · E B. What is the ratio of the area of E F G H to the area ofABC D ? (A) 49 64 (B) 25 32 (C) 7 8 (D) √ 5 2 8 (E) √ 14 4 6. (#14, AMC 10A, 2008) Older television screens have an aspect ratio of 4 : 3. That is, the ratio of the width to the height is 4 : 3. The aspect ratio of many movies is not 4 : 3, so they are sometimes shown on a television screen by “letterboxing” – darkening strips of equal height at the top and bottom of the screen, as shown.