solve each equation find all solutions in the interval 0 2π)
leave your answers in the exact form.
a) sin θ = cos(2θ)
b) sin (2θ) + cos(2θ) = √2/2
c) cos^3 + cos^2 - 3 cosθ - 3 = 0
d) sin 5x - sin 3x = cos 4x
e)sin(3x) + sin^2(x) + cos^2(x) = tan^2(x) - sec^2(x)
Use your graphing calculator to find the solutions to the
following equation for
0° ≤ θ < 360°
by defining the left side and right side of the equation as
functions and then finding the intersection points of their graphs.
Make sure your calculator is set to degree mode. (Round your
answers to one decimal place. Enter your answers as a
comma-separated list. If there is no solution, enter NO
SOLUTION.)
3 sin2 θ + 1 = 5 sin θ
Consider the function on the interval (0, 2π).
f(x) = sin(x) cos(x) + 2
(a) Find the open interval(s) on which the function is
increasing or decreasing. (Enter your answers using interval
notation.)
increasing
( )
decreasing
( )
(b) Apply the First Derivative Test to identify all relative
extrema.
relative maxima
(x, y) =
(smaller x-value)
(x, y) =
( )
(larger x-value)
relative minima
(x, y) =
(smaller x-value)
(x, y) =
...
Consider the function on the interval (0, 2π). f(x) = sin(x)/ 2
+ (cos(x))^2 (a) Find the open intervals on which the function is
increasing or decreasing. (Enter your answers using interval
notation.) increasing decreasing (b) Apply the First Derivative
Test to identify the relative extrema. relative maximum (x, y) =
relative minimum (x, y) =
Let f be a differentiable function on the interval [0, 2π] with
derivative f' . Show that there exists a point c ∈ (0, 2π) such
that cos(c)f(c) + sin(c)f'(c) = 2 sin(c).
a.)Find the length of the spiral r=θ for 0 ≤ θ ≤ 2
b.)Find the exact length of the polar curve r=3sin(θ), 0 ≤ θ ≤
π/3
c.)Write each equation in polar coordinates. Express as a
function of t. Assume that r>0.
- y=(−9)
r=
- x^2+y^2=8
r=
- x^2 + y^2 − 6x=0
r=
- x^2(x^2+y^2)=2y^2
r=
Let X1,...,Xn ∼ Geo(θ).
(a) Find a 90% asymptotic confidence interval for θ.
(b) Find a 99% asymptotic lower confidence intervals for φ =
1/θ, the expected number of trials until the first success.