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Trig Functions of Real Numbers Lesson 2.4a The Unit Circle P(x, y) • Consider a circle with radius r = 1 θ 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 t s r 2 The Unit Circle The trig ratios for θ can tell us x and y Since r = 1 y sin t y 1 x cos t x 1 y tan t x P(x, y) • θ r=1 View Nspire Demo 3 Example 4 Given t 3 Then 1 3 w(t ) P , 2 2 y What are sin, cos, tan? What if x t Determine P(x, y) What are the trig functions? 4 Implications It is now possible to take functions of angles greater than 360 (2π) or less than -360 (-2π) Try these 7 cot 3 tan 12 cos 8 csc8.2 Use both Wrapping concept Calculator (watch angle mode) 5 Properties of Trig Functions Odd functions Even functions f(-x) = - f(x) This definition is also applied to non trig functions. f(-x) = f(x) Which of the trig functions are?? Odd Even 6 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 7 Assignment Lesson 2.4a Page 166 Exercises 1 – 47 odd 8