Presentation on theme: "Trig Functions of Real Numbers Lesson 2.4a. 2 The Unit Circle Consider a circle with radius r = 1 Wrap t onto the circumference Then w(t) is a function."— Presentation transcript:
2 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) t θ P(x, y) r = 1
3 The Unit Circle The trig ratios for θ can tell us x and y Since r = 1 θ P(x, y) r = 1 View Nspire Demo View Nspire Demo
4 Example Given Then What are sin, cos, tan? What if Determine P(x, y) What are the trig functions? x y
5 Implications It is now possible to take functions of angles greater than 360 (2 π ) or less than -360 (-2 π ) Try these Use both Wrapping concept Calculator (watch angle mode)
6 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.
7 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 2 π For tan and ctn The period is π