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Trig Functions of Real Numbers Lesson 2.4a

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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

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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

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

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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)

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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.

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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

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8 Assignment Lesson 2.4a Page 166 Exercises 1 – 47 odd

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Objective: use the Unit Circle instead of a calculator to evaluating trig functions How is the Unit Circle used in place of a calculator?

Objective: use the Unit Circle instead of a calculator to evaluating trig functions How is the Unit Circle used in place of a calculator?

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