Trigonometric functions
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Trigonometric functions

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Trigonometric functions Trigonometric functions Presentation Transcript

  • Adult electrocardiogramTrigonometricFunctions
  • Trigonometric Functions:Periodic functions are functions that repeat exactly in regular intervals called cycles . Thelength of the cycle is called its period .
  • The amplitude of sine and cosine functions ishalf of the difference between the maximumand minimum values of the function. Theamplitude is always positive.Characteristics of the Graphs of Sine and Cosine
  • You can use the parent functions to graph transformations y = a sin bx and y = a cos bx.• Recall that a indicates a vertical stretch (⎪a⎥ > 1) or compression (0 < ⎪a⎥ < 1) , whichchanges the amplitude.• If a is less than 0, the graph is reflected across the x-axis.• The value of b indicates a horizontal stretch or compression, which changes the period.Transformations of Sine and Cosine GraphsExample:Using f (x) = sin x as a guide, graph the functiong(x) = 3 sin 2x. Identify the amplitude andperiod.
  • Frequency is the number of cycles in a given unit of time, so it is the reciprocal of the periodof a function.FrequencyExample:Sine and cosine can also be translated as y = sin (x - h) + k and y = cos (x - h) + k. Recall that avertical translation by k units moves the graph up (k > 0) or down (k < 0) .• A phase shift is a horizontal translation of a periodic function. A phase shift of h unitsmoves the graph left (h < 0) or right (h > 0) .Phase shift
  • Using f (x) = sin x as a guide, graphg(x) = sin (x + π /2 ) . Identify the x-interceptsand phase shift.Example:You can combine the transformations of trigonometric functions. Use the values ofa, b, h, and k to identify the important features of a sine or cosine function.Note: