The Trigonometric Functions

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© 2010 Pearson Education Inc.Goldstein/Schneider/Lay/Asmar, CALCULUS AND ITS APPLICATIONS, 12e– Slide 1 of 39 Chapter 8 The Trigonometric Functions.

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Presentation transcript:

The Trigonometric Functions Chapter 8 The Trigonometric Functions Copyright © 2014, 2010, 2007 Pearson Education, Inc.

Copyright © 2014, 2010, 2007 Pearson Education, Inc. Chapter Outline Radian Measure of Angles The Sine and the Cosine Differentiation and Integration of sin t and cos t The Tangent and Other Trigonometric Functions Copyright © 2014, 2010, 2007 Pearson Education, Inc.

Radian Measure of Angles Section 8.1 Radian Measure of Angles Copyright © 2014, 2010, 2007 Pearson Education, Inc.

Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section Outline Radians and Degrees Positive and Negative Angles Converting Degrees to Radians Determining an Angle Copyright © 2014, 2010, 2007 Pearson Education, Inc.

Copyright © 2014, 2010, 2007 Pearson Education, Inc. 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 1 radian. To convert degrees to radians, multiply the number of degrees by π/180. Copyright © 2014, 2010, 2007 Pearson Education, Inc.

Copyright © 2014, 2010, 2007 Pearson Education, Inc. Radians and Degrees Copyright © 2014, 2010, 2007 Pearson Education, Inc.

Copyright © 2014, 2010, 2007 Pearson Education, Inc. 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 Copyright © 2014, 2010, 2007 Pearson Education, Inc.

Copyright © 2014, 2010, 2007 Pearson Education, Inc. Converting Degrees to Radians EXAMPLE Convert the following to radian measure SOLUTION Copyright © 2014, 2010, 2007 Pearson Education, Inc.

Copyright © 2014, 2010, 2007 Pearson Education, Inc. Determining an Angle EXAMPLE Give the radian measure of the angle described. SOLUTION 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, Copyright © 2014, 2010, 2007 Pearson Education, Inc.