Trig Functions of Real NumbersThe Unit CircleSlide 3ExampleImplicationsProperties of Trig FunctionsTrig Functions are PeriodicAssignmentTrig Functions of Real NumbersLesson 2.4a2The 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)•tθP(x, y)r = 1t s rq q= = �=3The Unit CircleThe trig ratios for θcan tell us x and ySince r = 1•θP(x, y)r = 1sin1cos1tanyt yxt xytx= == ==View NspireDemoView NspireDemo4ExampleGivenThenWhat are sin, cos, tan?What ifDetermine P(x, y) What are the trig functions? 431 3( ) ,2 2tw t Pp=� �- -=� �� �� �xyt p=-5Implications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)( ) ( )7cot tan 12 cos 8 csc8.23pp p� �-� �� �6Properties of Trig FunctionsOdd functionsf(-x) = - f(x)Even functionsf(-x) = f(x)Which of the trig functions are?? Odd EvenThis definition is also applied to non trig functions.7Trig 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 π8AssignmentLesson 2.4aPage 166Exercises 1 – 47