1. Copyright © 2011 Pearson, Inc. 4.3 Trigonometry Extended: The Circular Functions Goals: Solve problems involving trigonometric functions. Memorize the 16-Point Unit Circle.

2. Copyright © 2011 Pearson, Inc. Slide 4.3 - 2 What you’ll learn about Trigonometric Functions of Any Angle Trigonometric Functions of Real Numbers Periodic Functions The 16-point unit circle … and why Extending trigonometric functions beyond triangle ratios opens up a new world of applications.

3. Copyright © 2011 Pearson, Inc. Slide 4.3 - 3 Initial Side, Terminal Side

4. Copyright © 2011 Pearson, Inc. Slide 4.3 - 4 Positive Angle, Negative Angle

5. Copyright © 2011 Pearson, Inc. Quadrants What do quadrants and the Super Bowl have in common? Slide 4.3 - 5

6. Copyright © 2011 Pearson, Inc. Slide 4.3 - 6 Coterminal Angles Two angles in an extended angle-measurement system can have the same initial side and the same terminal side, yet have different measures. Such angles are called____________________.

7. Copyright © 2011 Pearson, Inc. Slide 4.3 - 7 Example Finding Coterminal Angles

8. Copyright © 2011 Pearson, Inc. Slide 4.3 - 8 Example Finding Coterminal Angles

9. Copyright © 2011 Pearson, Inc. Slide 4.3 - 9 Trigonometric Functions of any Angle

10. Copyright © 2011 Pearson, Inc. Slide 4.3 - 10 Example Evaluating Trig Functions Determined by a Point in QI

11. Copyright © 2011 Pearson, Inc. Slide 4.3 - 11 Example5: Evaluating More Trig Functions

12. Copyright © 2011 Pearson, Inc. Slide 4.3 - 12 Example7a: Using one Trig Ratio to Find the Others

13. Copyright © 2011 Pearson, Inc. Slide 4.3 - 13 Example7b: Using one Trig Ratio to Find the Others

14. Copyright © 2011 Pearson, Inc. Slide 4.3 - 14 Unit Circle The unit circle is a circle of radius 1 centered at the origin.

15. Copyright © 2011 Pearson, Inc. Slide 4.3 - 15 The 16-Point Unit Circle

16. Copyright © 2011 Pearson, Inc. Refer to the unit circle shown. Which letter best represents the value given? cos -270° sin π/3 cos 4π/3 sin - 5π/4 tan 60°

17. Copyright © 2011 Pearson, Inc. Find the exact value of each of the following trig expressions. Try to give the result without looking at your unit circle.