1. Explain why the graphs of tangent and cotangent have vertical
asymptotes
2. Explain why the graphs of cosecant and secant have vertical
asymptotes
3. Sketch a graph of y=3sec(2x)y=3sec(2x) by hand, in other
words, without a graphing utility. Include 2 periods, and include
the asymptotes.
Create a table of all three of these trigonometric functions for
angles from 0 to 2p, with a spacing of 0.1 radian. Your table
should contain a column for the angle and then for the sine,
cosine, and tangent. ((python))
Analyticity of trigonometric functions (a) Directly from the
definition, construct the Taylor Series centered at x = 0 for the
function f(x) = cos(x). (b) Show that this series converges for all
x ∈ R. (c) Show that this series converges to cos(x) for all x ∈
R.
Sketch the asymptotes of the Bode plot magnitude and phase for
the transfer functions:
1. T(s) = 2000/(s(s+200))
2. T(s) = 100/(s(.1s+1)(.5s+1))
3. T(s) = 1/(s(s+1)(.02s+1))
Sketch the asymptotes of the Bode plot magnitude and phase for
the transfer functions:
1. T(s) = 1/((s+1)^2+(s+10)^2)
2. T(s) = (s+5)(s+10)/((s)(s+1)(s+100))
for loop practice – Taylor Series!The moment you finish
implementing the trigonometric functions, you realize that you have
forgotten your favorite function: the exponential! The Taylor
Series for the exponential function is
푒푥=1+푥1!+푥22!+푥33!+...,‒∞<푥<∞a) Using a for loop, compute and
display the error of the Taylor series when using 12 and 15 terms,
each as compared to the exponential function when evaluated at x =
2. b) Can you figure out how to compute and display the number of
terms necessary...
Utilize identities to calculate the exact value of the five
remaining trigonometric functions if:
csc(α)= √3, π/2, < α < π
Calculate the equivalent algebraic expression for:
sec(arcsin(x - 1)