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:
- Equation menu
- explicit
- implicit
- point
- anchor
- Animation menu
- Families on Inventory.
- Two
- 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))
- Change scales on X axis to show "pi".
- Plot the point (h, sin(h))
- Plot the point
(h, Asin(Bh+C))
- 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.]
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.
- Find
the smallest positive A and B so that y=Acos(Bx) with y(0)=10,
y(pi/3)=10.
- Find
the smallest positive C where y=cos(x + C) with y(-pi/3)=1.
- Find an
estimate for any and all x in [-3,3] where 2sin(x) +
3cos(2x) = 1.
- Find
the smallest positive A, B and C so that y=Acos(Bx +C) has amplitude 3,
period 2 and y(-1)=3.