The Derivatives of Trigonometric Functions

The Derivatives of Trigonometric Functions - 18.01 Calculus...

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18.01 Calculus Jason Starr Fall 2005 Lecture 6. September 20, 2005 Homework. Problem Set 2 Part I: (f)–(j); Part II: Problems 1, 3 and 4. Practice Problems. Course Reader: 1J-1, 1J-2, 1J-3, 1J-4 1. Trigonometric functions. What is angle ? For a sector of a unit circle (a circle of radius 1), the angle of the sector equals both the length of the arc of the sector and 1 / 2 the area of the sector. Although we have as yet general definitions of neither arc length nor area, this can be used to give a rigorous definition of angle. We can divide any sector in two equal pieces: simply bisect the chord of the sector. We also know how to add two angles, by laying the sectors in adjacent positions. Denoting the area of a unit circle by the symbol π (which happens to be the familiar π ), these 2 operations produce every angle of the form mπ/ 2 n , with m and n integers. Every angle can
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18.01 Calculus Jason Starr Fall 2005 be approximated arbitrarily well by such angles. Thus, for every continuous function of an angle, every value of the function can
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