Math 115  Lab #7
M. Flashman

I. Understanding Linear Parameters  in Graphs of Trig (sine and cosine) Functions
• Amplitude
• Period
• Phase Shift
II. Graphs of Tangent and Secant Functions.
III. Moodle Reporting of work.

• Tools for Winplot used in this lab:
• explicit
• implicit
• point
• anchor
• Families on Inventory.
• Two
• Intersections...
• View ... grid.... pi on scales

I.Graphs of Trig Functions

• Circles and the graphs of sin(x) vs Asin(Bx+C): [review in part]
• Set the parameters: A= 1 and B=1.
• Use implicit to graph the equation xx + yy = 1
• Use implicit to graph the equation xx + yy = AA
• Plot the point (cos(h), sin(h))
• Plot the point (Acos(Bh+C), Asin(Bh+C))
• Use animator A and  h.
• Change scales on X axis to show "pi".
• Plot the point (h, sin(h))
• Plot the point (h, Asin(Bh+C))
• Use animator A and  h.
• Plot graphs with explicit for
• y = f(x) = sin(x)
• y = g(x) = Asin(Bx+C)
• Use animator A; family A.
• Set A = 1, use animator for B; family B.[See graph SinAX]
• Set B = 1, use animator for C;  family C.[See A sin(B(X+C))]
• Notes:
• The amplitude of the function g is |A|.
• The period of the function g is |2pi/B|. [That is g(x + 2pi/B) = g(x). ]
• The phase shift of the function g is -C/B. [That is g(-C/B) = 0.]

• Finding Parameters and Solving equations
• Find the smallest positive A and B where y=Acos(Bx) with y(0)=5, y(pi/2)=5.
• Find the smallest positive C where y=cos(x + C) with y(-pi/4)=1.
• Find an estimate for any and all x  in [-3,3] where  3sin(x) + 2cos(3x) = 4.

II. Graphs of Tangent and Secant Functions.
Explorations:
• Look at tangent and secant functions with winplot.
• Discuss the period for these functions.
• Compare secant with cosine;  tangent with sine and cosine.
• Use identities to explain period for tangent.

III. Record your answers for the next work and submit them on Moodle by Wednesday, APRIL 7th.

1. Find the smallest positive A and B so that y=Acos(Bx) with y(0)=10, y(pi/3)=10.
2. Find the smallest positive C where y=cos(x + C) with y(-pi/3)=1.
3. Find an estimate for any and all x  in [-3,3] where  2sin(x) + 3cos(2x) = 1.
4. Find the smallest positive A, B and C so that y=Acos(Bx +C) has amplitude 3, period 2 and y(-1)=3.

End of Lab 7