Trig Functions of Real Numbers Lesson 2.4a

The Unit Circle Consider a circle with radius r = 1 Wrap t onto the circumference Then w(t) is a function which wraps t to a point P(x, y) Also, t translates to θ (radians) P(x, y) • t θ r = 1

The Unit Circle The trig ratios for θ can tell us x and y Since r = 1 P(x, y) • θ r = 1 View Spreadsheet Demo

Example Given Then What if What are sin, cos, tan? Determine P(x, y) What are the trig functions? x y

Implications It is now possible to take functions of angles greater than 360 (2π) or less than -360 (-2π) Try these Use both Wrapping concept Calculator (watch angle mode)

Properties of Trig Functions Odd functions f(-x) = - f(x) Even functions f(-x) = f(x) Which of the trig functions are?? Odd Even This definition is also applied to non trig functions.

Trig Functions are Periodic The functions repeat themselves The period is the smallest value, p for which f(x) = f(x + p) For sin, cos, sec, csc The period is 2π For tan and ctn The period is π

Assignment Lesson 2.4a Page 166 Exercises 1 – 47 odd