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Chapter8

# Chapter8 - Chapter 8 The Trigonometric Functions Chapter...

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Chapter 8 The Trigonometric Functions

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Radian Measure of Angles The Sine and the Cosine Differentiation and Integration of sin t and cos t The Tangent and Other Trigonometric Functions Chapter Outline
§ 8.1 Radian Measure of Angles

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Radians and Degrees Positive and Negative Angles Converting Degrees to Radians Determining an Angle Section Outline
Goldstein/SCHNIEDER/LAY, CALCULUS AND ITS APPLICATIONS , 11e – Slide #5 Radians and Degrees The central angle determined by an arc of length 1 along the circumference of a circle is said to have a measure of one radian .

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Goldstein/SCHNIEDER/LAY, CALCULUS AND ITS APPLICATIONS , 11e – Slide #6 Radians and Degrees
Goldstein/SCHNIEDER/LAY, CALCULUS AND ITS APPLICATIONS , 11e – Slide #7 Positive & Negative Angles Definition Example Positive Angle : An angle measured in the counter-clockwise direction Definition Example Negative Angle : An angle measured in the clockwise direction

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Goldstein/SCHNIEDER/LAY, CALCULUS AND ITS APPLICATIONS , 11e – Slide #8 Converting Degrees to Radians EXAMPLE EXAMPLE SOLUTION SOLUTION Convert the following to radian measure ( 29 ( 29 . 210 450 ° - ° b a ( 29 2 5 radians 180 450 450 π π = × = ° a ( 29 6 7 radians 180 210 210 π π - = × - = ° - b
Goldstein/SCHNIEDER/LAY, CALCULUS AND ITS APPLICATIONS , 11e – Slide #9 Determining an Angle EXAMPLE EXAMPLE SOLUTION SOLUTION Give the radian measure of the angle described. The angle above consists of one full revolution (2π radians) plus one half- revolutions (π radians). Also, the angle is clockwise and therefore negative. That is, ( 29 . 3 2 π π π - = + - = t

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§ 8.2 The Sine and the Cosine
Sine and Cosine Sine and Cosine in a Right Triangle Sine and Cosine in a Unit Circle Properties of Sine and Cosine Calculating Sine and Cosine Using Sine and Cosine Determining an Angle t The Graphs of Sine and Cosine Section Outline

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Goldstein/SCHNIEDER/LAY, CALCULUS AND ITS APPLICATIONS , 11e – Slide #12 Sine & Cosine
Goldstein/SCHNIEDER/LAY, CALCULUS AND ITS APPLICATIONS , 11e – Slide #13 Sine & Cosine in a Right Triangle

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Goldstein/SCHNIEDER/LAY, CALCULUS AND ITS APPLICATIONS , 11e – Slide #14 Sine & Cosine in a Unit Circle
Goldstein/SCHNIEDER/LAY, CALCULUS AND ITS APPLICATIONS , 11e – Slide #15 Properties of Sine & Cosine

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Goldstein/SCHNIEDER/LAY,
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