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Trig Functions of Real Numbers

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.

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Trig Functions of Real Numbers

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  1. Trig Functions of Real Numbers Lesson 2.4a

  2. The Unit Circle • Consider a circle with radius r = 1 • Wrap t onto thecircumference • Then w(t) is a functionwhich wraps t to a point P(x, y) • Also, t translates to θ (radians) • P(x, y) t θ r = 1

  3. The Unit Circle • The trig ratios for θcan tell us x and y • Since r = 1 • P(x, y) θ r = 1 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 (2π) or less than -360 (-2π) • Try these • Use both • Wrapping concept • Calculator (watch angle mode)

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

  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 2π • For tan and ctn • The period is π

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

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