522020 MyOpenMathhttpswww.myopenmath.comassess2cid.docx

5/2/2020 MyOpenMath
https://www.myopenmath.com/assess2/?cid=69772&aid=497570
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Chapter 7 Review Courtney Garrity
Question 1 0/10 pts 5 99
Rewrite in terms of and
Next Question
cos(x + )
π
3
sin(x) cos(x)
Question Help: Video
Solve for the smallest positive solution.
x =

Give your answer accurate to two decimal places.
Next Question
sin(5x)cos(9x) − cos(5x)sin(9x) = − 0.45
Rewrite as
A =
=
Note: should be in the interval
Next Question
−5 sin(x) + 1 cos(x) A sin(x + ϕ)
ϕ
ϕ −π < ϕ < π
Write the product as a sum:
18 cos(41w)cos(15w) =
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Next Question
Write the sum as a product:
Next Question
cos(23.6s) − cos(8.6s) =
Find all solutions to on
=
Give your answers as a list separated by commas
Next Question
cos(7x) − cos(x) = sin(4x) 0 ≤ x <
2π
3
x

Simplify to an expression involving a single trigonometric
function.
Next Question
sin(6w) − sin(4w)
cos(6w) + cos(4w)
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Solve for the four smallest positive solutions
=
Give your answers accurate to at least two decimal places, as a
list separated by commas
Next Question
sec(4x) − 6 = 0

x
Solve for all solutions
=
Give your answers accurate to 2 decimal places, as a list
separated by commas
Next Question
4 sin2(x) − 10 sin(x) + 4 = 0 0 ≤ x < 2π
x
=
Give your answers accurate to 2 decimal places, as a list
separated by commas
Next Question
8 sin2(t) − 2 cos(t) − 5 = 0 0 ≤ t < 2π
t
If , x in quadrant I, then �nd (without �nding x)

sin x =
2
5
sin(2x) =
cos(2x) =
tan(2x) =
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Next Question
=
Give your answers accurate to at least 2 decimal places, as a list
separated by commas

Next Question
4 sin(2ϕ) + 2 cos(ϕ) = 0 0 ≤ ϕ < 2π
ϕ
=
Give your answers accurate to at least 2 decimal places, as a list
separated by commas
Next Question
6 cos(2β) = 6 cos2(β) − 1 0 ≤ β < 2π
β
Question Help: Video Video
If for then
Next Question
csc(x) = 4, 90 ∘ < x < 180 ∘ ,
sin( ) =
x

2
cos( ) =
x
2
tan( ) =
x
2
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A population of rabbits oscillates 33 above and below average
during the year, hitting the lowest
value in January (t = 0). The average population starts at 750
rabbits and increases by 120 each
year. Find an equation for the population, P, in terms of the
months since January, t.
=
Next Question

P(t)
-
-
-
-
a.
b.
c.
d.
Match each graph with it's equation type:
Next Question
(mx + b)sin(5x)
ab
x + sin(5x)
sin(5x) + mx + b
(abx)sin(5x)
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Find an equation of the form that �ts the data below
x 0 1 2 3
y 6 34 150 746
To �t the data:
a =
b =
c =
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y = abx + c sin( x)π
2
Find all solutions of the equation
The answer is and where is any integer, ,
, ,
, .
Next Question
2 cos x − 1 = 0.
A + Bkπ C + Dkπ k 0 < A < C < 2π

A = B =
C = D =
For use a double-angle or half-angle formula to simplify the
equation and
then �nd all solutions of the equation in the interval
The answers are
,
,
and
with .
Next Question
sin 2x + cos x = 0,
[0, 2π).
x1 =
x2 =
x3 =
x4 =
x1 < x2 < x3 < x4
Question Help: Worked Example 1

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Find all solutions of the equation
The answer is and where is any integer, ,
, ,
, .
Next Question
2 sin x + √3 = 0.
A + Bkπ C + Dkπ k 0 < A < C < 2π
A = B =
C = D =
Find all solutions of the equation in the interval
The answer is , and
with .

Next Question
2 sin2 x − cos x = 1 [0, 2π).
x1 = x2 = x3 =
x1 < x2 < x3
Find all solutions of the equation in the interval
The answer is , and
with .
Next Question
2 cos 3x = 1 [0, π).
x1 = x2 = x3 =
x1 < x2 < x3
Convert the polar coordinate to Cartesian coordinates.
Enter exact values.
x =
y =
(8, )
π
6

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Next Question
Convert the Cartesian coordinate (2, 5) to polar coordinates, .
r =
Enter an exact value.
=
Next Question
0 ≤ θ < 2π
θ
Simplify to a single trig function.

Next Question
1 + sin(t)
1 + csc(t)
Simplify to an expression involving a single trig function with
no fractions.
Next Question
sin2(t) + cos2(t)
sin2(t)
Simplify to a single trig function.
Next Question
sin(t)
sec(t) − cos(t)
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Simplify and write the trigonometric expression in terms of sine
and cosine:
. =
1 + cos y
1 + sec y
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Assignment 8.3-8.4: Polar Coordinates and Graphs Courtney
Garrity
(20, 393°)
(-20, 213°)
(-20, -147°)
(20,-327°)
(-20, -393°)
(20, 213°)

Which points are the same as (20, 33°)?
. Check all that apply.
Next Question
Enter exact values.
x =
y =
Next Question
(6, )
3π
4
x =
y =
Next Question
(7, )
11π
6

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Convert the Cartesian coordinate (3, 1) to polar coordinates, .
r =
Enter an exact value.
=
Next Question
0 ≤ θ < 2π
θ
Convert the Cartesian coordinate (5, 4) to polar coordinates,
r =
Enter exact value.

=
Next Question
0 ≤ θ < 2π
θ
Convert the Cartesian coordinate (6, -3) to polar coordinates,
r =
Enter exact value.
=
Next Question
0 ≤ θ < 2π
θ
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Rewrite the Cartesian equation as a polar equation.
=
Enter theta for if needed.
Next Question
x = − 1
r(θ)
θ
Rewrite the polar equation as a Cartesian equation.
Next Question
r = 4 cos(θ)
Rewrite the Cartesian equation y = 5x2 as a polar equation.
r(θ) =
Enter theta for θ if needed.
Next Question

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Write a polar equation for the graph below. Enter theta for
`theta` if needed.
1 2 3 4-1-2-3-4
1
2
3
4
-1
-2
-3
-4
`r(theta)` =
Next Question
A curve with polar equation `r=frac(36 )(9 sin theta+37 cos

theta)`
represents a line. This line has a Cartesian equation of the form
`y = mx + b` ,where `m` and
`b` are constants. Give the formula for `y` in terms of `x`. For
example, if the line had equation
`y = 2x+3` then the answer would be `2*x + 3`.
y =
Next Question
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-
-
-
-
a. `r=5+4 cos(theta)`
b. `r=9+4 cos(theta)`
c. `r=1+4 cos(theta)`
d. `r=4+4 cos(theta)`

e. `r=4 cos(theta)`
Match each graph with its equation
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-
Next Question
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-
-
-
-
a. `r=cos(2 theta)`
b. `r=cos(5 theta)`

c. `r=sin(6 theta)`
d. `r=cos(6 theta)`
e. `r=cos(7 theta)`
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-
Next Question
1 2 3 4-1-2-3-4
1
2
3
4
-1
-2
-3
-4

Which of the following is the equation for the graph shown
above?
`r=1+2 sin(theta)`
`r=3 cos(3 theta)`
`r=3 cos(2 theta)`
`r=1+2 cos(theta)`
`r=3 sin(2 theta)`
Next Question
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-
1 2 3 4-1-2-3-4
1
2
3
4
-1
-2
-3
-4

-
1 2 3 4-1-2-3-4
1
2
3
4
-1
-2
-3
-4
-
1 2 3 4-1-2-3-4
1
2
3
4
-1
-2
-3
-4
-
1 2 3 4-1-2-3-4
1
2
3
4

-1
-2
-3
-4
a. `r=3 sin(2 theta)`
b. `r=1+2 sin(theta)`
c. `r=3 cos(2 theta)`
d. `r=1+2 cos(theta)`
e. `r=3 cos(3 theta)`
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-
1 2 3 4-1-2-3-4
1
2
3
4

-1
-2
-3
-4
Next Question
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- `r=theta sin(theta)`
- `r= 5/sqrt(theta)`
- `r=5 sin(theta/2)`
- `r = 1+3 cos(3 theta)`
a.
b.
c.
d.
Match each equation with its graph
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Section 8.4 Courtney Garrity
Question 1 0/1 pt 2 99
Write the vector shown above in component form.
Vector =
Note: In the graph, each box is 1 unit by 1 unit in size
Next Question
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Vector
-
-
-

-
-
Vector Combination
a.
b.
c.
d.
e.
u
v
q
r
s
t p
Match the vectors with one of the combinations of the and
vectors from
the graph.
Next Question
→p, →q , →r, →s, and →t →u →v

→r
→t
→p
→s
→q
3→u − →v
3→u
→v − 2→u
−→v
→u + →v
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u
v
Write the vector shown below as a combination of vectors and

shown above
Vector = +
Note: In both graphs, each box is 1 unit by 1 unit in size
Next Question
→u →v
→u →v
A vector with magnitude 3 points in a direction 310 degrees
counterclockwise from the positive x
axis.
Write the vector in component form.
Vector =
Give each value accurate to at least 1 decimal place
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Next Question
Given the vector , �nd the magnitude and angle in which the
vector points
(measured counterclockwise from the positive x-axis, )
=
=
Next Question
→u = ⟨ − 4, − 1⟩
0 ≤ θ < 2π
||→u||
θ
Question Help: Video Video Video Video
A person leaves home and walks 5 miles west, then 2 miles
southwest.
How far from home is she?
miles
In what direction must she walk to head directly home?
degrees North of East

Next Question
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A person starts walking from home and walks:
3 miles East
6 miles Southeast
4 miles South
5 miles Southwest
2 miles East
This person has walked a total of miles
Find the total displacement vector for this walk:
If this person walked straight home, they'd have to walk miles
Next Question
Three di�erent forces act on an object. They are:
Find the net force on the object (the sum of the forces)

Find what fourth force, would need to be added so the object
feels no force, that is, so
=
Next Question
→F 1 = < − 4, 3 >
→F 2 = < − 6, − 2 >
→F 3 = < 1, − 5 >
Fnet
Fnet =
F4
Fnet = 0
F4
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An airplane is heading north at an airspeed of 800 km/hr, but
there is a wind blowing from the
northeast at 50 km/hr.
The plane will end up �ying degrees o� course
The plane's speed relative to the ground will be km/hr
Next Question
An airplane needs to head due north, but there is a wind
blowing from the southwest at 60
km/hr. The plane �ies at an airspeed of 500 km/hr,
To end up due north, the pilot will need to �y the plane
degrees
west of north
Next Question
As part of video game, the point (6,1) is rotated
counterclockwise about the origin through an
angle of 20 degrees.
Find the new coordinates of this point
x =

y =
Next Question
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Two children are throwing a ball back-and-forth straight across
the back seat of a car. The ball is
being thrown 7 mph relative to the car, and the car is travelling
25 mph down the road.
If one child doesn't catch the ball and it �ies out the window, in
what direction does the ball �y
(ignoring wind resistance)?
degrees, measured relative to the car's forward direction
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Evaluate the expression and write the result in the form .
Next Question
√−9 a + bi
Next Question
√−3√−27 a + bi
Next Question
(1 + 7i) + (4 − 5i) a + bi

Next Question
( − 6 − 8i) − ( − 3 − i) a + bi
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Next Question
( − 1 − 3i)(4 − 2i) a + bi
Next Question
1 + 2i

7i
a + bi
Divide:
5 - 5i
3 + 6i
. Write your answer in a + bi form
Next Question
Rewrite the complex number `2 e^(1.5 i)` in `a + b i` form
Next Question
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Write the following numbers in the polar form `re^(i theta)`, `0
le theta < 2pi `:

(a) ` frac(1)(6)`
` r = ` , ` theta = ` ,
(b) ` 3 + 3 i`
` r = ` , ` theta = ` ,
(c) ` - 7 + 7 i`
` r = ` , ` theta = ` .
Next Question
Calculate `(-2+i)^6`. Give your answer in `a + b i` form
Next Question
Calculate `sqrt(-4+4i)`. Give your answer in `a + b i` form.
Give the solution with smallest
positive angle.
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Eliminate the parameter to �nd a simpli�ed Cartesian equation
of the form for
The Cartesian equation is =
Next Question
t y = mx + b
{
x(t) = 8 − t
y(t) = − 3 − 4t
y
Given the parametric equations below, eliminate the parameter t
to obtain an equation for y as a
function of x
=
Next Question
{

x(t) = 3√t
y(t) = 8t + 4
y(x)
Eliminate the parameter t to �nd a Cartesian equation in the
form for:
The resulting equation can be written as =
Next Question
x = f(y)
{
x(t) = − 4t2
y(t) = − 7 + 1t
x
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Given the parametric equations below, eliminate the parameter t
to obtain an equation for y as a
function of x
=
Next Question
{
x(t) = e4t
y(t) = e7t
y(x)
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-
1 2 3 4 5-1-2-3-4-5
1
2
3
4
5
-1

-2
-3
-4
-5
-
1 2 3 4 5-1-2-3-4-5
1
2
3
4
5
-1
-2
-3
-4
-5
-
1 2 3 4 5-1-2-3-4-5
1
2
3
4
5
-1
-2
-3
-4
-5

-
1 2 3 4 5-1-2-3-4-5
1
2
3
4
5
-1
-2
-3
-4
-5
a.
b.
c.
d.
e.
Match equation graph with its parametric equation. Not all
equations will be used. All graphs
shown for −5 ≤ t ≤ 5
{
x(t) = t + cos(t)
y(t) = t + sin(t)

{
x(t) = t cos(t)
y(t) = t sin(t)
{
x(t) = t3
y(t) = t2
{
x(t) = t3 − t
y(t) = t2
{
x(t) = t2
y(t) = t3
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Next Question
1 2 3 4 5-1-2-3-4-5

1
2
3
4
5
-1
-2
-3
-4
-5
The graph below can be represented by parametric equations of
the form
Where a = and b =
Next Question
{
x(t) = a cos(t)
y(t) = b sin(t)
The ellipse can be drawn with parametric equations where is
written in the
form
with r =
and y(t) =

Next Question
+ = 1
x2
22
y2
32
x(t)
x(t) = r cos(t)
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Suppose parametric equations for the line segment between and
have the
form:
If the parametric curve starts at when and ends at at , then
�nd ,
, , and .

Next Question
(6, − 10) (9, 3)
{
x(t) = a + bt
y(t) = c + dt
(6, − 10) t = 0 (9, 3) t = 1 a
b c d
a =
b =
c =
d =
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1 2 3 4 5 6-1-2-3-4-5-6
1
2

3
4
5
6
-1
-2
-3
-4
-5
-6
The plot above is created with the parametric equations
x(t) = a cos(bt)
y(t) = c sin(dt)
To acheive this graph,
a =
b =
c =
d =
Hint: b and d are both whole numbers from 1 to 3
Next Question
{
Question Help: Video Video Video Video
A bicycle wheel has radius `R`. Let P be a point on the spoke of

a wheel at a distance `d` from
the center of the wheel. The wheel begins to roll to the right
along the the x-axis. The curve
traced out by `P` is given by the following parametric
equations:
` {( x(theta) = 25 theta - 15 sin(theta)), (y(theta) = 25 - 15
cos(theta) ) :} `
What must we have for `R` and `d`?
`R` =
`d` =
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-
-
-
-
Determine the shape of each polar curve.
Next Question
r =
8
1 + 3 sin(θ)
r =
8
3 + sin(θ)
r = 8
r =
8
1 + sin(θ)
Given the polar equation ,

The eccentricity is
The equation of the directrix is:
The shape of the curve is: Select an answer
Next Question
r =
8
6 − 3 cos(θ)
e =
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Write a polar equation for a conic having focus at the origin,
directrix , and eccentricity
.
Type theta for .
Next Question
x = − 2

e = 5
r =
θ
Sketch a graph of . Use the graph to write a Cartesian equation
for the conic.
Next Question
r =
40
4 − 6 cos(θ)
Sketch a graph of . Use the graph to write a Cartesian equation
for the conic.
r =
16
5 − 3 sin(θ)
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Assignment 7.5: Solving Trigonometric Equations Courtney
Garrity

Find all solutions to on the interval .
=
Give your answers as exact values in a list separated by
commas.
Next Question
2 sin(θ) = 1 0 ≤ θ < 2π
θ
Find all solutions to on the interval .
=
commas.
Next Question
2 cos(θ) = − √3 0 ≤ θ < 2π
θ

Solve for , .
=
Give your answers as values rounded to at least two decimal
places in a list separated by
commas.
Next Question
t 0 ≤ t < 2π
18 sin(t)cos(t) = 12 cos(t)
t
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Solve for all solutions .
=

commas.
Next Question
2 cos2(x) + 3 cos(x) + 1 = 0 0 ≤ x < 2π
x
=
Give your answers as values accurate to at least two decimal
commas.
Next Question
12 sin2(w) − 7 sin(w) + 1 = 0 0 ≤ w < 2π
w
=
commas.

Next Question
4 sin2(x) − 13 sin(x) − 12 = 0 0 ≤ x < 2π
x
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=
commas.
Next Question
cos2(w) = − 4 sin(w) 0 ≤ w < 2π
w
Solve on .

There are two solutions, A and B, with A < B.
A =
B =
Give your answers accurate to 3 decimal places.
Next Question
sin(x) = 0.34 0 ≤ x < 2π
Solve on .
There are two solutions, A and B, with A < B.
A =
B =
Give your answers accurate to 3 decimal places.
Next Question
cos(x) = − 0.87 0 ≤ x < 2π
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Solve for the smallest three positive solutions.
list separated by commas.
Next Question
8 cos(5x) = 5
Solve for the four smallest positive solutions.
=
Next Question
3 sin( x) = 2π
3
x

=
Give your answers accurate to at least 2 decimal places and in a
Next Question
2 sin(2α) − 3 sin(α) = 0 0 ≤ α < 2π
α
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=
Give your answers accurate to at least 2 decimal places and in a

Next Question
6 cos(2w) = 6 cos2(w) − 4 0 ≤ w < 2π
w
Solve 2sin2(x) + sin(x) - 1 = 0 for all solutions.
x = +2kπ ; Select an answer
commas.
Next Question
Solve `2cos^2(w)+5cos(w)+3 = 0` for all solutions.
`w` = where Select an answer
Give your answer as an exact value.
Next Question
Solve `2cos^2(x)-cos(x)-3 = 0` for all solutions.
`x` = where `k in ZZ`

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Chapter 10 Review Courtney Garrity
Find the standard form for the equation of a circle
with a diameter that has endpoints and .
Next Question
(x − h)
2
+ (y − k)
2
= r2
( − 1, 1) (7, 5)
h =
k =

r =
Recall the equation for a circle with center and radius . At what
point in the �rst quadrant
does the line with equation intersect the circle with radius 4
and center (0, 5)?
=
=
Enter your answer correct to 3 decimal places .
Next Question
(h, k) r
y = 0.5x + 5
x
y
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Find the focus, directrix, focal diameter, vertex and axis of
symmetry for the parabola:
The focus is …
COM205: Week 9 Assignment Page 1
` Course Project Part 4: Written Speech Final
Assignment Overview
Over the past few weeks, you have conducted research and
created a rough outline and submitted a draft for your speech.
Based upon the feedback provided from the draft you have
already created for this project, you will prepare your final copy
by end of day Sunday for instructor grading.
This is the fourth of a five-part project to compose and present
a persuasive or informative speech. You will present the final
speech to your instructor only, in Week 11, via YouTube video.
Review the Course Project Details to review the timeline of
deliverables and the descriptions of the different parts of the
project.
Assignment Details:
Perform the following tasks:
· Create a minimum 1-page (250 words) written final speech in
Word to be submitted by the end of Week 9.
· Include/adhere to the following in your written speech:
· Title page.
· Written speech (portion you will deliver in Part 4).
· Reference page using APA style.
· Summary regarding feedback received from your instructor on
your initial draft and how it was incorporated into your final
speech (5-7 sentences).
· Double-spaced, Times New Roman, 12pt font.

Hints: Refer to the following resource located on the Internet to
help you paraphrase, summarize, or quote your source materials.
· Purdue OWL – Click on “Using Research” in the left
navigation; click on “Quoting, Paraphrasing, and Summarizing.”
Grading:
Gradable items in assignment followWritten Assignment Rubric
Points
Completed the following as directed:
Organization
40
Content of speech
60
Feedback summary
20
Style
10
Writing Conventions
10
Total Points
140
` Course Project Part 3: Written Speech Draft
Assignment Overview
Over the past few weeks, you have created a rough outline and
conducted research for writing your speech. Based upon what
you have already created for this project, you will write a draft
of your speech to be submitted to your instructor by the end of
the day Sunday for feedback. You will then have the
opportunity to incorporate feedback in the next part of this
project.

This is the third of a five-part project to compose and present a
persuasive or informative speech. You will present the final
project.
Assignment Details:
· Create a minimum 1-page (250 words) written draft speech in
Word to be submitted by the end of Week 8.
· Include/adhere to the following in your written speech:
· Title page.
· Written speech (portion you will deliver in Part 4).
· Reference page using APA style.
· Summary regarding feedback received from your instructor on
your initial draft and how it was incorporated into your final
speech (5-7 sentences).
· Double-spaced, Times New Roman, 12pt font.
Hints: Refer to the following resource located on the Internet to
help you paraphrase, summarize, or quote your source materials.
Grading:
Gradable items in assignment followWritten Assignment Rubric
Points
Completed the following as directed:
Organization
40
Content of speech
60
Feedback summary
20
Style
10
Writing Conventions

10
Total Points
140
` Course Project Part 2: Resources and References
Assignment Overview
Your speech should incorporate at least two resources of
information, which you paraphrase, summarize, and/or quote.
Using LIRN and the Internet, identify at least two sources of
information that will be used to support your speech. At least
one of these resources of information must be obtained through
the LIRN online library resource.
This is the second of a five-part project to compose and present
a persuasive or informative speech. You will present the final
project.
Assignment Details:
· Create a 2-page (500 words) Word document outlining your
resources (see below) to be submitted by the end of Week 6.
· Develop a Reference page.
· Include the following:
· Paraphrase, summarize, and/or quote information you will use
in your speech from no less than two resources.
· Explain how you will use this information to support your
main and supporting topics within your speech.
· Consider using this Source Materials and Reference List
worksheet to assist you with this part of your project. This
worksheet does not need to be turned in to your instructor.

· Provide a reference list in proper APA style.
Hints: Locate thefollowing resources on the Internet to help you
format the references page and paraphrase, summarize, and/or
quote the information from your sources. Your instructor can
help you determine the best sources to use.
· Citation Machine – automated citing and referencing of
sources.
Grading:
Gradable items in assignment
Points
Correctly paraphrase, summarize, or quote from two resources.
50
Explained how information from resources supports speech.
50
Used proper APA style for citations and for references.
20
Error-free grammar, spelling, punctuation.
10
Correct formatting – double-spacing, Times New-Roman, 12pt
font.
10
Total Points
140
` Course Project Part 1: Speech Outline
Assignment Overview
For your speech outline, you will begin compiling ideas for
your speech and consider how you can use research to support

you in developing your speech. Possible topics include an
aspect related to your field of study, topics in the news, or any
other topics of interest. Keep in mind that talking about what
you know and are passionate about can make the speech easier
to write, as well as present.
This is the first of a five-part project to compose and present a
persuasive or informative speech. You will present the final
project.
Assignment Details:
· Create a 1-2 page (250-500 word) speech outline in Word to
be submitted by the end of Week 4.
· Include the following in your outline:
· Main topic summary – Briefly describe the main topic you will
be presenting in your speech (3-5 sentences).
· Background – Briefly describe why you chose your topic (3-5
sentences).
· Speech type – Define if your speech will be informative,
persuasive, or entertaining.
· Supporting topics – Briefly discuss at least three supporting
topics (i.e. subtopics) that will be discussed in your speech (3-5
sentences).
· Conclusion – Summarize the main points of your speech and
the angle or position that you plan on taking (5-7 sentences).
· References - Brainstorm and briefly describe three ways
references found via your research will help in writing and
delivering your speech (3-5 sentences).
Hint: Review the Speech Grading Guidelines to get an idea of
how your final speech will be graded.
Grading:
Gradable items in assignment
Points
Summarized main topic in brief but adequate detail.

30
Provided background explanation of topic.
30
Defined clearly speech type.
15
Articulated clearly supporting topics (i.e. subtopics).
15
Provided conclusion summarizing main points.
15
Described three ways references provided help.
15
Error-free grammar, spelling, punctuation.
10
Correct formatting – double-spacing, Times New-Roman, 12pt
font.
10
Total Points
140

522020 MyOpenMathhttpswww.myopenmath.comassess2cid.docx

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