Math 115 Lab 7-10-03

Math 115 Lab M. Flashman 7-10-03

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

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?