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The Trigonometric Functions

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Presentation on theme: "The Trigonometric Functions"— Presentation transcript:

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

2 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.

3 Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Section 8.2 The Sine and the Cosine Copyright © 2014, 2010, 2007 Pearson Education, Inc.

4 Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Section Outline 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 Copyright © 2014, 2010, 2007 Pearson Education, Inc.

5 Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Sine & Cosine Copyright © 2014, 2010, 2007 Pearson Education, Inc.

6 Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Sine & Cosine in a Right Triangle Copyright © 2014, 2010, 2007 Pearson Education, Inc.

7 Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Sine & Cosine in a Unit Circle Copyright © 2014, 2010, 2007 Pearson Education, Inc.

8 Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Properties of Sine & Cosine Copyright © 2014, 2010, 2007 Pearson Education, Inc.

9 Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Calculating Sine & Cosine EXAMPLE Give the values of sin t and cos t, where t is the radian measure of the angle shown. SOLUTION Since we wish to know the sine and cosine of the angle that measures t radians, and because we know the length of the side opposite the angle as well as the hypotenuse, we can immediately determine sin t. Since sin2t + cos2t = 1, we have Copyright © 2014, 2010, 2007 Pearson Education, Inc.

10 Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Calculating Sine & Cosine CONTINUED Replace sin2t with (1/4)2. Simplify. Subtract. Take the square root of both sides. Copyright © 2014, 2010, 2007 Pearson Education, Inc.

11 Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Using Sine & Cosine EXAMPLE If t = 0.4 and a = 10, find c. SOLUTION Since cos(0.4) = 10/c, we get Copyright © 2014, 2010, 2007 Pearson Education, Inc.

12 Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Determining an Angle t EXAMPLE Find t such that –π/2 ≤ t ≤ π/2 and t satisfies the stated condition. SOLUTION One of our properties of sine is sin(-t) = -sin(t). And since -sin(3π/8) = sin(-3π/8) and –π/2 ≤ -3π/8 ≤ π/2, we have t = -3π/8. Copyright © 2014, 2010, 2007 Pearson Education, Inc.

13 Copyright © 2014, 2010, 2007 Pearson Education, Inc.
The Graph of Sin(t) Copyright © 2014, 2010, 2007 Pearson Education, Inc.

14 Copyright © 2014, 2010, 2007 Pearson Education, Inc.
The Graphs of Sine & Cosine Copyright © 2014, 2010, 2007 Pearson Education, Inc.

15 Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Incorporating Technology Copyright © 2014, 2010, 2007 Pearson Education, Inc.


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