1. Trig Functions of Any Angle Lesson 2.3

2. Angles Beyond 90°  Expand from the context of angles of a right triangle  Consider a ray from the origin through a given point (x, y) (x, y) r θ

3. Reference Triangle  Drop a perpendicular from (x,y) to the x-axis This forms a reference triangle (x, y) θ β Click to view spreadsheet example

4. Angles in Different Quadrants  Note that x and y have different signs in the various quadrants Thus the trig functions will have different signs for the quadrants  For each quadrant, determine the sign of the functions I II III IV (x, y) θ

5. Angles in Different Quadrants  Remember "allsintancos" I II III IV all positive sin is positive tan is positive cos is positive

6. Standard Angles  Recall table of functions of basic angles  Now we can expand this table

7. Standard Angles 090120135150180270360 sin cos tan almost 90° 120° 135° 150° 180°

8. Assignment  Lesson 2.3  Page 154  Exercises 1 – 71 Odd