Understanding Trigonometric Functions of Any Angle

1. 4.4 Trig Functions of Any Angle Objectives: Evaluate trigonometric functions of any angle Use reference angles to evaluate trig functions

2. Trig Functions of Any Angle Given an angle  in standard position with (x,y) a point on the terminal side of  y (x,y)  r x 4.4 Trigonometric Functions of Any Angle

3. Example 1 • Let (-3,4) be a point on the terminal side of . Find the sine, cosine and tangent of . 4.4 Trigonometric Functions of Any Angle

4. Example 2 • Given • Find sin  and sec  4.4 Trigonometric Functions of Any Angle

5.   ’  ’ ’ Reference Angles • Let  be an angle in standard position. Its reference angle is the acute angle ’ formed by the terminal side of  and the x-axis. 4.4 Trigonometric Functions of Any Angle

6.   ’  ’ ’ Calculating Reference Angles 4.4 Trigonometric Functions of Any Angle

7. Example 3 • Find the reference angle ’ •  = 300° •  = 2.3 •  = -135° 4.4 Trigonometric Functions of Any Angle

8. Evaluating Trig Functions of Any Angle To find the value of a trig function of any angle : • Evaluate the function for the associated reference angle ’. • Determine the sign of the trig function based on the quadrant in which  lies. 4.4 Trigonometric Functions of Any Angle

9. Example 4 • Use reference angles to evaluate the trig function 4.4 Trigonometric Functions of Any Angle

10. Example 5 • Let  be an angle in Quadrant II such that sin =1/3. Find cos  and tan  by using trig identities. 4.4 Trigonometric Functions of Any Angle

11. Closure • Explain how to use reference angles to determine trig functions of any angle 4.4 Trigonometric Functions of Any Angle

12. Assignment • 4.4 page 320: 3-102 every 3rd, 111, 112 4.4 Trigonometric Functions of Any Angle

13. 4  7 Bellwork • Find sin  • Determine the sign (positive or negative) of the six trig functions for angles in Quadrant I, Quadrant II, Quadrant III, and Quadrant IV 4.4 Trigonometric Functions of Any Angle