Trig Functions of Any Angle Lesson 2.3
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
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
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
Angles in Different Quadrants Remember "allsintancos" I II III IV all positive sin is positive tan is positive cos is positive
Standard Angles Recall table of functions of basic angles Now we can expand this table
Standard Angles sin cos tan almost 90° 120° 135° 150° 180°
Assignment Lesson 2.3 Page 154 Exercises 1 – 71 Odd