MAT129 Fall 2025 Notes
mathnstuff.com/math/precalc/MAT129fa25/p.16.htm
© 11/3/2025   A2, Agnes Azzolino
Graphs of Trigonometric Functions & f(x)= Asin(Bx - C) + D. Text 8.1,8.2, PG. 642, 659

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Welcome to Precalc!
Hi,
    In the text, pg 772 - 787, you are to "Determine the amplitude, period, midline, phase shift and an equation involving cosine for the graph shown ..."
    You have worked with this idea before and will need it in the future as in the curve shifting, reflections, and other composition coded in y = af(bx-c)+d.
    Contact me through the pink box on www.mathnstuff.com/math/math.htm or with the phone number on your class CANVAS home page.
    Stay safe, A2
Trig Children Functions
A -- Amplitude and vertical stretching/compressing factor.
If |A|>1 curve stretched. If |A|<1, curve is compressed.
If A is negative, curve is reflected/flipped over the midline.
B -- Period and horizontal stretching/compressing factor
The period is 2pi/B for the sine and cosine.
The period is pi/B for the tangent.
If B is negative, the curve is reflected about a vertical axis.
  ex. sin(1x) has a period of 2pi.
  ex. sin(2x) "goes twice as fast" and has a period of 2pi/2 or pi -- compressed.
  ex. sin(x/4) "goes four times as slow" and has a period of 2pi/(.25) or 8pi -- stretched.
C -- phase shifter if c = 0, no shift; if c>0, shift is c/B to the left; if c<0, shift is c/B to right
D -- midline shifter
If D = 0 curve's midline is y= 0.
If D = 0, curve's midline shifts up to y = D.
If D < 0, curve's midline shifts down to y = - D.


  Input an angle A in degrees in the yellow box, then press each button to compute angle A in radians, its sine, cosine, and tangent.
  A is °
 
  is rad
  is
  is
  is
      the reciprocal, the cosecant, is
  is 		  the reciprocal, the secant, is
  is 		  the reciprocal, cotangent, is
  is
  Input an angle B in radians in the yellow box, then press each button to compute angle B in degrees, its sine, cosine, and tangent.
  B is radians;
 
  is °
  is
  is
  is
      the reciprocal, the cosecant, is
  is 		  the reciprocal, the secant, is
  is 		  the reciprocal, cotangent, is
  is

The reader
must round
each result.