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)

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• 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?