1. Chapter 6 – Trigonometric Functions: Right Triangle Approach 6.3 - Trigonometric Functions of Angles

2. Let POQ be a right triangle with an acute angle  where  is in standard position. The point P is on the terminal side of . 6.3 - Trigonometric Functions of Angles P(x, y) y x r Q O x y

3. Definition of Trigonometric Functions Let  be an angle in standard position and let P(x, y) be a point on the terminal side. If is the distance from the origin to the point P(x, y), then 6.3 - Trigonometric Functions of Angles

4. Quadrantal Angles Quadrantal Angles are angles that are coterminal with the coordinate axis. 6.3 - Trigonometric Functions of Angles

5. Remember: Signs of the Trig Functions QuadPositive Functions Negative Functions I All None II sin, csccos, sec, tan, cot III tan, cotsin, csc, cos, sec IV cos, secsin, csc, tan, cot 5.2 - Trigonometric Function of Real Numbers

6. Examples – pg. 460 Find the quadrant in which  lies from the information given. 6.3 - Trigonometric Functions of Angles

7. Reference Number Let  be an angle in standard position. The reference angle   associated with  is the acute angle formed by the terminal side of  and the x- axis. 5.1 - The Unit Circle

8. Evaluating Trig Functions for Any Angle To find the values of the trigonometric functions for any angle , we carry out use the following steps: 1. Find the reference angle   associated with the angle . 2. Determine the sign of the trigonometric function of  by noting the quadrant in which  lies. 3. The value of the trigonometric function of  is the same, except possibly for sign, as the value of the trigonometric function of  . 5.1 - The Unit Circle

9. Examples – pg. 459 Find the reference angle for the given angle. 6.3 - Trigonometric Functions of Angles

10. Examples – pg. 459 Find the exact value of the trigonometric function. 6.3 - Trigonometric Functions of Angles

11. Fundamental Identities Reciprocal Identities Pythagorean Identities 5.2 - Trigonometric Function of Real Numbers

12. Examples – pg. 460 Write the first trigonometric function in terms of the second for  in the given quadrant. 6.3 - Trigonometric Functions of Angles

13. Examples – pg. 460 Find the given values of the trigonometric functions of  from the information given. 6.3 - Trigonometric Functions of Angles

14. Area of a Triangle The area A of a triangle with sides of length a and b with included angle  is 6.3 - Trigonometric Functions of Angles

15. Examples – pg. 460 6.3 - Trigonometric Functions of Angles

16. Examples – pg. 460 6.3 - Trigonometric Functions of Angles