1. Copyright © 2011 Pearson, Inc. 4.2 Trigonometric Functions of Acute Angles

2. Copyright © 2011 Pearson, Inc. Slide 4.2 - 2 What you’ll learn about Right Triangle Trigonometry Two Famous Triangles Evaluating Trigonometric Functions with a Calculator Applications of Right Triangle Trigonometry … and why The many applications of right triangle trigonometry gave the subject its name.

3. Copyright © 2011 Pearson, Inc. Slide 4.2 - 3 Standard Position An acute angle θ is in standard position, when one ray is along the positive x-axis, the vertex is at the origin, and the other ray extends into the first quadrant.

4. Copyright © 2011 Pearson, Inc. Slide 4.2 - 4 Trigonometric Functions

5. Copyright © 2011 Pearson, Inc. Slide 4.2 - 5 Example Evaluating Trigonometric Functions of 45 º Find the values of all six trigonometric functions for an angle of 45 º.

6. Copyright © 2011 Pearson, Inc. Slide 4.2 - 6 Example Evaluating Trigonometric Functions of 45 º Find the values of all six trigonometric functions for an angle of 45 º.

7. Copyright © 2011 Pearson, Inc. Slide 4.2 - 7 Example Evaluating Trigonometric Functions of 60 º Find the values of all six trigonometric functions for an angle of 60º.

8. Copyright © 2011 Pearson, Inc. Slide 4.2 - 8 Example Evaluating Trigonometric Functions of 60 º Find the values of all six trigonometric functions for an angle of 60º.

9. Copyright © 2011 Pearson, Inc. Slide 4.2 - 9 Common Calculator Errors When Evaluating Trig Functions Using the calculator in the wrong angle mode (degree/radians) Using the inverse trig keys to evaluate cot, sec, and csc Using function shorthand that the calculator does not recognize Not closing parentheses

10. Copyright © 2011 Pearson, Inc. Slide 4.2 - 10 Example Solving a Right Triangle

11. Copyright © 2011 Pearson, Inc. Slide 4.2 - 11 Example Solving a Right Triangle

12. Copyright © 2011 Pearson, Inc. Slide 4.2 - 12 Quick Review 1. Solve for x. x 3 2 2. Solve for x. 6 3 x

13. Copyright © 2011 Pearson, Inc. Slide 4.2 - 13 Quick Review

14. Copyright © 2011 Pearson, Inc. Slide 4.2 - 14 Quick Review Solutions 1. Solve for x. x 3 2 2. Solve for x. 6 3 x

15. Copyright © 2011 Pearson, Inc. Slide 4.2 - 15 Quick Review Solutions