Math 115 Lab M. Flashman
71003

Compare:

graph of sin(x) with graph of sin(x)

graph of cos(x) with graph of cos(x)

graph of tan(x) with graph of tan(x)

graph of sec(x) with graph of sec(x)

graph of sin(x) with graph of sin(x + 2pi)

graph of cos(x) with graph of cos(x + 2pi)

graph of tan(x) with graph of tan(x + pi)

Graphs of sine: Discuss how
each constant A, B, and C effects the graph.[>1, >0, <0.]

f(x)= Asin(x) Use animator; family

f(x)= sin(Bx) Use animator; family. See
graph
SinAX

f(x)= sin(x+C) Use animator; family

f(x)= Asin(Bx+C) Use animator; family. See
graph A
sin(BX+C)

Graphs of cosine Discuss
how each constant A, B, and C effects the graph.[>1, >0, <0.]

f(x)= Acos(x) Use animator; family

f(x)= cos(Bx) Use animator; family

f(x)= cos(x+C) Use animator; family

f(x)= Acos(Bx+C) Use animator; family.

Graphs of tangent Discuss
how each constant A, B, and C effects the graph.[>1, >0, <0.]

f(x)= Atan(x) Use animator; family

f(x)= tan(Bx) Use animator; family

f(x)= tan(x+C) Use animator; family

f(x)= Atan(Bx+C) Use animator; family

Solving equations for trig

Find A and B if y=Acos(Bx) with y(0)=20, y(pi/2)=20.
Are these unique?

Find x if 3sin(x) + 2cos(3x) = 4 ; slider,
table, solver

Solving equations with exponential and logarithmic functions

Find A and k if y=Ae^(kx) with y(1)=20, y(2)= 50.

Find x if ln(x) +ln(x+1) = 5 ; slider, table, solver

Logarithmic scales

Y= log(a), X= log(a) family a = 1 to 100 11 steps

Y= log(Ab^x) = xlog(b)+ log(A) : log linear scales

Y = log(Ax^p) = plog(x)+log(A) : log log scales
(log(t), log(a*t^b))

Tangents to graphs for logs and exponential functions.??
A precalculus view.

Y = exp(rt) : Y is value of investment of $1.00 with
continuously compounded interest at r per annum.

Y = exp(ra) + r*exp(ra)*(a  t) : Y
is value of investment of exp(ra) invested at time t = a
with simple interest at r per annum.

What if r = 1 ( 100%)?

What do these graphs with r = 1 look like when reflected across
the line Y= X?