Step 2 - Your page to turn in!.sagews

Your turn!

1. Follow the link http://mathbits.com/MathBits/TISection/Statistics2/sinusoidal.htmlto find data for the two other cities. Type in the data and create separate scatter plots. Then find the sinusoidal model for each.

2. Plot the function: f(x)=sin(2x-π)-2, g(x)=-3sec(πx); h(x)=tan(x-π/2) in a single graphing window from [-2π,2π]. Use different colors for each graph!

Washington weather data (month, max temp): (1, 43),(2,47),(3,56),(4,67),(5,75),(6,84),(7,88),(8,87),(9,80),(10,68),(11,58),(12,47)

data=[(1, 43),(2,47),(3,56),(4,67),(5,75),(6,84),(7,88),(8,87),(9,80),(10,68),(11,58),(12,47)]
p=scatter_plot(data)
p

data=[(1, 43),(2,47),(3,56),(4,67),(5,75),(6,84),(7,88),(8,87),(9,80),(10,68),(11,58),(12,47)]
a,b,c,d=var('a,b,c,d')
model(x)=a * sin(b*(x - c))+d
values=find_fit(data,model,initial_guess=(20,pi/6,7,45))
params=[a,b,c,d]
for i in range(4):
    params[i]=values[i].rhs()

model(x)=params[0] * sin(params[1]*(x - params[2]))+params[3]
model(x)
p=scatter_plot(data,xmin=-2,xmax=14,ymin=-10,ymax=100)
p+=plot(model(x),xmin=-2,xmax=14,ymin=-10,ymax=100)
p

22.750416372761766*sin(0.4941622527603166*x + 4.33616519835939) + 65.36784858935329

find_fit(data,model,initial_guess=(20,pi/6,7,45))

Error in lines 1-1 Traceback (most recent call last): File "/cocalc/lib/python2.7/site-packages/smc_sagews/sage_server.py", line 1013, in execute exec compile(block+'\n', '', 'single') in namespace, locals File "", line 1, in <module> File "sage/misc/lazy_import.pyx", line 354, in sage.misc.lazy_import.LazyImport.__call__ (/ext/sage/sage-8.0/src/build/cythonized/sage/misc/lazy_import.c:3559) return self.get_object()(*args, **kwds) File "/ext/sage/sage-8.0/local/lib/python2.7/site-packages/sage/numerical/optimize.py", line 685, in find_fit raise ValueError("no variables given") ValueError: no variables given

y=a * sin(b*(x - c))+d
show(y)

$\displaystyle a \sin\left(-b {\left(c - x\right)}\right) + d$

Austin weather data (month, max temp): (1,62),(2,65),(3,72),(4,80),(5,87),(6,92),(7,96),(8,97),(9,91),(10,82),(11,71),(12,63)

data=[(1,62),(2,65),(3,72),(4,80),(5,87),(6,92),(7,96),(8,97),(9,91),(10,82),(11,71),(12,63)]
p=scatter_plot(data)
p

data=[(1,62),(2,65),(3,72),(4,80),(5,87),(6,92),(7,96),(8,97),(9,91),(10,82),(11,71),(12,63)]
a,b,c,d=var('a,b,c,d')
model(x)=a * sin(b*(x - c))+d
values=find_fit(data,model,initial_guess=(20,pi/6,7,45))
params=[a,b,c,d]
for i in range(4):
    params[i]=values[i].rhs()

model(x)=params[0] * sin(params[1]*(x - params[2]))+params[3]
model(x)
p=scatter_plot(data,xmin=-2,xmax=14,ymin=-10,ymax=100)
p+=plot(model(x),xmin=-2,xmax=14,ymin=-10,ymax=100)

17.75774360770287*sin(0.5034536935229376*x - 2.004686232497934) + 79.14960706079732

plot(x * sin(x), (x, -2, 10)), g(x)=-3sec(πx); h(x)=tan(x-π/2)

*** WARNING: Code contains non-ascii characters *** *** WARNING: Code contains possible implicit multiplication *** *** Check if [u'2x', u'3sec('] need a "*" sign for multiplication, e.g. < 5x > should be < 5*x > ! *** Error in lines 1-1 Traceback (most recent call last): File "/cocalc/lib/python2.7/site-packages/smc_sagews/sage_server.py", line 1013, in execute exec compile(block+'\n', '', 'single') in namespace, locals File "<string>", line 1 plot(x * sin(x), (x, -Integer(2), Integer(10)))f(x)=sin(2x-π)-Integer(2), g(x)=-3sec(πx); __tmp__=var("x"); h = symbolic_expression(tan(x-π/Integer(2))).function(x) ^ SyntaxError: invalid syntax