MATH1200ES31
Welcome to the permanent home page
for Section ES31 of MATH1200 (Trigonometry)
at Southeast Community College
in the Fall term of 2020.
I am Toby Bartels, your instructor.
Course administration:
 Canvas page
(where you must log in).
 Help with DjVu
(if you have trouble reading the files on this page).
 Course policies (TBA).
 Class hours:
Mondays, Wednesdays, and Fridays from 10:00 to 10:50
in ESQ 100D.
 Class Zoom meeting:
92861572182.
 Final exam time:
December 11 Friday from 10:00 to 11:40
in ESQ 100D.
Contact information:
Readings
The official textbook for the course
is the 11th Edition of Algebra & Trigonometry
by Sullivan published by PrenticeHall (Pearson).
You will automatically get an online version of this textbook through Canvas,
although you can also order a print version if you like.
This comes with access to Pearson MyLabs,
directly integrated into Canvas),
on which many of the assignments appear.
Basic trigonometry
 General review:
 Reading from the textbook: Section 2.1 (pages 150–153).
 Exercises due on August 26 Wednesday:
 In which number quadrant are both coordinates positive?
 Write down a formula for the distance between
the points (x_{1}, y_{1})
and (x_{2}, y_{2})
in a rectangular coordinate system.
 If the two short sides of a right triangle have lengths 3 and 4,
then what is the length of the hypotenuse?
 Exercises from the textbook due on August 28 Friday:
2.1.19, 2.1.21, 2.1.23, 2.1.25, 2.1.27,
2.1.31, 2.1.39, 2.1.41, 2.1.43.
 Circles:
 Reading from the textbook: Section 2.4 (pages 185–188).
 Exercises due on August 28 Friday:
 Fill in the blank:
The distance from the centre (or center) of a circle to any point on the circle
is the _____ of the circle.
 Write down an equation in the variables x and y
for a circle
whose centre is (h, k) and whose radius is r.
(This will be an equation
in which x, y, h, k, and r all appear.)
 If
x^{2} + y^{2} = r^{2}
is the equation of a circle in x and y,
then what are the coordinates of the centre of the circle?
 Exercises from the textbook due on August 31 Monday:
2.4.5, 2.4.9, 2.4.11, 2.4.13, 2.4.15, 2.4.17,
2.4.21, 2.4.23, 2.4.25, 2.4.27.
 Angles:
 Reading from the textbook:
Section 7.1 through Objective 4 (pages 518–524).
 Exercises due on August 31 Monday:
 If a central angle in a circle
subtends an arc whose length equals the circle's radius,
then what is the measure of that angle?
 How many radians is 360°?
 Exercises from the textbook due on September 2 Wednesday:
7.1.11, 7.1.13, 7.1.15, 7.1.17, 7.1.19, 7.1.21,
7.1.23, 7.1.26, 7.1.35, 7.1.37.
 Length and area with radians:
 Reading from the textbook:
The rest of Section 7.1 (pages 524–526).
 Exercises due on September 2 Wednesday:
Fill in the blanks with algebraic expressions:
 In a circle of radius r,
a central angle whose measure is θ radians
subtends an arc whose length is s = ___;
 In a circle of radius r,
a central angle whose measure is θ
forms a sector whose area is A = ___;
 Around a circle of radius r,
an object with an angular speed of ω
has a linear speed of v = ___.
 Exercises from the textbook due on September 4 Friday:
7.1.71, 7.1.73, 7.1.79, 7.1.81, 7.1.87, 7.1.91, 7.1.95, 7.1.99.
 Right triangles:
 Reading from the textbook: Section 7.2 (pages 531–538).
 Exercises due on September 4 Friday:
 Fill in the blank:
The sine of the complement of θ is the _____ of θ.
 If θ is the measure of an acute angle in a right triangle,
then what is the cotangent of θ
as a ratio of the lengths
of the adjacent leg, the opposite leg, and/or the hypotenuse?
 If the secant of an angle is 3,
then what is its cosine?
 Exercises from the textbook due on September 9 Wednesday:
7.2.9, 7.2.10, 7.2.11, 7.2.12, 7.2.13, 7.2.15, 7.2.17, 7.2.23, 7.2.27, 7.2.31,
7.2.33, 7.2.37, 7.2.39, 7.2.41, 7.2.43, 7.2.45, 7.2.57, 7.2.65.
 Special angles:
 Reading from the textbook:
Section 7.3 through Objective 2 (pages 543–546).
 Exercise due on September 9 Wednesday:
Write down the exact values
of the sine, cosine, tangent, cotangent, secant, and cosecant
of π/6 (or 30°), π/4 (or 45°), and π/3 (or 60°).
(This is 18 values to write down in all,
which you might put into a handy table.
One way or another, be sure to label which value is which.)
 Exercises from the textbook due on September 11 Friday:
7.3.7, 7.3.19, 7.3.21, 7.3.23, 7.3.27, 7.3.29.
 Applications with acute angles:
 Reading from the textbook:
The rest of Section 7.3 (pages 546–549).
 Exercises due on September 11 Friday:
 If you want to calculate the secant of 50 degrees
on a calculator with buttons only for sine, cosine, and tangent,
then what do you enter on the calculator?
 If you know
the horizontal distance to the base of an object
and the angle of elevation to the top of the object
and you want to find the height of the object,
then would you use
the sine, the cosine, or the tangent of the angle of elevation?
 Exercises from the textbook due on September 14 Monday:
7.3.31, 7.3.33, 7.3.35, 7.3.59, 7.3.69, 7.3.73, 7.3.79.
 General angles:
 Reading from the textbook:
Section 7.4 through Objective 5 (pages 555–561).
 Exercises due on September 14 Monday:
 Two angles that differ by one or more full turns
are called _____ angles.
 If the six fundamental trigonometric functions
all have the same absolute values at θ as at α
and α is an acute angle,
then α is the _____ angle of θ.
 Which of the six fundamental trigonometric functions of θ
are positive
when θ terminates in Quadrant III?
 Exercises from the textbook due on September 16 Wednesday:
7.4.11, 7.4.15, 7.4.17, 7.4.21, 7.4.31, 7.4.33, 7.4.39,
7.4.51, 7.4.53, 7.4.57, 7.4.59, 7.4.61, 7.4.75.
 Circular trigonometry:
 Reading from the textbook:
 The rest of Section 7.4 (page 562);
 Section 7.5 through "Trigonometric Functions of Angles"
(pages 566–570).
 Exercises due on September 16 Wednesday:
 Suppose that you start at the point (1, 0)
in a rectangular coordinate system
and move in the direction towards (0, 1) along the unit circle,
for a total distance t.
(This is the usual thing, not a trick question.)
If you end at the point (a, b),
express sin t, cos t, tan t,
cot t, sec t, and csc t
using only a and b.
 Now instead of moving along the unit circle (with radius 1),
move along a circle of radius r (but still centred at the origin).
That is, start at (r, 0)
and move along the circle in the direction of (0, r)
for a total distance of s,
and let θ be s/r.
(This is again the usual thing for a nonunit radius.)
Now if you end at the point (x, y),
express sin θ, cos θ,
tan θ, cot θ,
sec θ, and csc θ
using only x, y, and r.
 Exercises from the textbook due on September 18 Friday:
7.4.83, 7.4.87, 7.4.93, 7.5.11, 7.5.13, 7.5.17, 7.5.19, 7.5.23,
7.5.31, 7.5.33, 7.5.39, 7.5.41, 7.5.47, 7.5.49.
 The trigonometric functions:
 Reading from the textbook:
The rest of Section 7.5 (pages 570–575).
 Exercises due on September 18 Friday:
 Most of the six trigonometric functions have a period of 2π;
which two have a period of π instead?
 Consider the numbers 2 and 1/2.
Which is in the range of the sine function,
and which is in the range of the cosecant function?
 Out of 0, π/2, π, and 2π,
which is not
in the domain of the tangent function?
 Exercises from the textbook due on September 21 Monday:
7.5.63, 7.5.65, 7.5.69, 7.5.81, 7.5.85, 7.5.87, 7.6.3.
Quiz 1, covering the material in Problem Sets 1–10,
is available on September 25 Friday.
Advanced trigonometry
 Basic sinusoidal graphs:
 Reading from the textbook:
 Section 7.6 through the box before Example 1 (pages 579&580);
 Section 7.6 Objective 2 through the box before Example 3
(pages 581&582).
 Exercises due on September 21 Monday:
Each of these questions has infinitely many answers;
either list enough that the pattern is clear in both directions,
or use a formula involving an arbitrary integer k.
 What are the intercepts of the graph of the sine function?
 What are the turning points (local max and min)
of the graph of the sine function?
 What are the intercepts of the graph of the cosine function?
(Be careful not to miss one!)
 What are the turning points
of the graph of the cosine function?
 Exercises from the textbook due on September 23 Wednesday:
7.6.6, 7.6.8, 7.6.11, 7.6.13.
 More basic graphs:
 Reading from the textbook:
 Section 7.7
through
"The Graph of the Cotangent Function y = cot x"
(pages 594–596);
 Section 7.7 Objective 3 (pages 597&598).
 Exercises due on September 23 Wednesday:
 What are the intercepts of the graph of the tangent function?
 What are the intercepts of the graph of the cotangent function?
 What are the linear asymptotes
to the graphs of the tangent and secant functions?
 What are the linear asymptotes
to the graphs of the cotangent and cosecant functions?
 Exercises from the textbook due on September 25 Friday:
7.7.3, 7.7.6, 7.7.7, 7.7.10, 7.7.11, 7.7.12, 7.7.13, 7.7.16.
 Coordinate transformations:
 Review from (mostly) the textbook:
 Exercises due on September 28 Monday:
Assume that the axes are oriented in the usual way
(positive xaxis to the right, positive yaxis upwards).
 Fill in the blank with a direction:
To change the graph of y = f(x)
into the graph of y = f(x − 1),
shift the graph to the ___ by 1 unit.
 To change the graph of y = f(x)
into the graph of y = −f(x),
do you reflect the graph left and right or up and down?
 To change the graph of y = f(x)
into the graph of y = f(2x),
do you compress or stretch the graph
left and right?
 Exercises from the textbook due on September 30 Wednesday:
3.5.5, 3.5.6, 3.5.19, 3.5.21, 3.5.23, 3.5.25, 3.5.29, 3.5.30,
3.5.33, 3.5.35, 3.5.53, 3.5.41, 3.5.45, 3.5.61.
 Transformations of trigonometric functions:
 Reading from the textbook:
 Section 7.6 Objective 1 Examples 1&2 (pages 580&581);
 Section 7.6 Objective 2 Example 3 (page 582);
 Section 7.7 Objective 2 (pages 596&597);
 Section 7.7 Objective 4 (pages 598&599).
 Exercises due on September 30 Wednesday:
Suppose that f is a periodic function with period T.
(For example, f might be the sine function,
so that T would be 2π,
or f might be the tangent function, so that T would be π.
But answer the questions in general, referring to T.)
 What is the period (as a function of x)
of f(x) + 2?
 What is the period of f(2x)?
 What is the period of 2f(x)?
 Exercises from the textbook due on October 2 Friday:
7.6.23–32, 7.7.17, 7.7.21, 7.7.23, 7.7.25, 7.7.29, 7.7.31.
 Sinusoidal functions:
 Reading from (mostly) the textbook:
 My handout on sinusoidal functions
(DjVu);
 The rest of Section 7.6 (pages 582–588);
 Section 7.8 Objective 1 (pages 601–605).
 Exercises due October 2 Friday:
 If f(x) =
A sin(ωx)
for all x,
with A > 0 and ω > 0,
then what are the amplitude and period of f?
 If f(x) = A sin x + B
for all x,
with A > 0,
then what are the maximum and minimum values of f?
 If f(x) =
sin(ωx − φ)
for all x,
with 0 ≤ φ < 2π,
then what is the phase shift of f?
 Exercises from the textbook due on on October 5 Monday:
7.6.35, 7.6.39, 7.6.51, 7.6.57, 7.6.61, 7.6.87,
7.8.9, 7.8.11, 7.8.19, 7.8.17.
 Inverse trigonometric operations:
 Reading from the textbook:
 Section 8.1 through Objective 7 (pages 622–630);
 Section 8.2 through Objective 2 (pages 653–637).
 Exercises due on October 5 Monday:
Fill in all of these blanks with algebraic expressions (or constants).
Work only in the real number system.
 That y = sin^{−1} x
means that x = ___ and ___ ≤ y ≤ ___.
 cos^{−1} x exists
if and only if ___ ≤ x ≤ ___.
 cos^{−1} cos θ =
θ
if and only if ___ ≤ θ ≤ ___.
 Exercises from the textbook due on October 7 Wednesday:
8.1.19, 8.1.21, 8.2.11, 8.2.13, 8.2.19, 8.1.39, 8.1.41,
8.1.43, 8.1.45, 8.1.51, 8.1.53, 8.1.55, 8.1.57.
 More inverse trigonometric operations:
 Reading from (mostly) the textbook:
 Exercises due on October 7 Wednesday:
 cos sin^{−1} x = ___
(if either side exists).
 If f is the function given by
f(x) = sin^{−1} x,
then what is its inverse function f^{ −1}?
(Write down a formula
that involves one or more of the six basic trigonometric operations
and that includes all necessary conditions.)
 Exercises from the textbook due on October 9 Friday:
8.2.33, 8.2.35, 8.2.47, 8.2.49, 8.1.59,
8.1.61, 8.2.61, 8.2.63, 8.2.65.
 Sumangle formulas:
 Reading from the textbook:
Section 8.5 Objectives 1–3 (pages 659–666).
 Exercises due on October 9 Friday:
Fill in the blanks
with trigonometric expressions
in which each trigonometric operation that appears
is only applied directly to α or β.
 sin(α + β) = ___.
 cos(α + β) = ___.
 sin(α − β) = ___.
 cos(α − β) =
___.
 Exercises from the textbook due on October 12 Monday:
8.5.15, 8.5.17, 8.5.19, 8.5.21, 8.5.35,
8.5.37, 8.5.39, 8.5.41, 8.5.77.
 Doubleangle and related formulas:
 Reading from the textbook:
 Section 8.6 through Example 3 in Objective 2 (pages 672&675);
 Section 8.7 (pages 683–685).
 Exercises due on October 12 Monday:
 Express sin(2α)
using sin α and/or cos α.
 Express sin^{2} α
using sin(2α) and/or cos(2α).
 Express sin α sin β
using sin(α + β),
sin(α − β),
cos(α + β),
and/or cos(α − β).
 Factor sin α + sin β
so that each factor has at most one trigonometric operation.
 Exercises from the textbook due on October 14 Wednesday:
8.6.83, 8.6.85, 8.6.87, 8.7.7, 8.7.9, 8.7.11, 8.7.13,
8.7.15, 8.7.17, 8.7.19, 8.7.21, 8.7.23.
 Halfangle formulas:
 Reading from the textbook:
Section 8.6 Objective 3 (pages 676–678).
 Exercises due on October 14 Wednesday:
Fill in the blanks
with trigonometric expressions
in which each trigonometric operation that appears
is only applied directly to α.
Make sure that each expression
has at most one value for each value of α;
in other words, do not use ±.
 sin^{2}(α/2) = ___.
 cos^{2}(α/2) = ___.
 tan(α/2) = ___
(notice not squared).
 Exercises from the textbook due on October 16 Friday:
8.6.25, 8.6.29, 8.6.23, 8.6.27, 8.6.9, 8.6.11,
8.6.13, 8.6.15, 8.6.17, 8.6.19.
 Simplifying trigonometric expressions:
 Reading from (mostly) the textbook:
 Exercises due on October 16 Friday:
 Fill in the blank with an expression
in which sin θ is the only trigonometric quantity:
cos^{2} θ = ___.
 Factor without using any trigonometric identities:
sin^{2} θ − 1 = (___)(___).
 If you regard a cosine as a square root,
then what expression is conjugate
to 1 − cos θ?
 Exercises from the textbook due on October 21 Wednesday:
8.4.1, 8.4.2, 8.4.6, 8.4.8, 8.4.11, 8.4.15, 8.4.17,
8.4.29, 8.4.55, 8.4.71, 8.4.95.
 Trigonometric equations:
 Reading from the textbook: Section 8.3 (pages 641–646).
 Exercises due on October 21 Wednesday:
 Write a general form
for the solutions of tan x = b
using tan^{−1} b
and an arbitrary integer k.
 Similarly,
give the general solution of sin x = b.
(This one is more complicated than the last one.)
 To obtain θ ∈ [0, 2π)
(that is, 0 ≤ θ < 2π),
what interval should 3θ belong to?
 Exercises from the textbook due on October 23 Friday:
8.3.13, 8.3.23, 8.3.25, 8.3.27, 8.3.37,
8.3.39, 8.3.109, 8.3.115.
 Tricky trigonometric equations:
 Reading from the textbook:
 Section 8.5 Objective 4 (pages 666–668);
 Section 8.6 Objective 2 Examples 4&5
(pages 675&676).
 Exercises due on October 23 Friday:
 Since you can factor x + xy
as x(1 + y),
how can you factor
cos θ +
sin θ cos θ?
 To solve
a sin θ +
b cos θ =
c
with the help of a sumangle formula,
what should you multiply both sides of the equation by?
 To solve
sin (aθ) +
sin (bθ) =
0,
how can you factor the lefthand side?
 Exercises from the textbook due on October 26 Monday:
8.3.61, 8.3.73, 8.5.93, 8.5.97, 8.6.75, 8.6.77, 8.7.47.
Quiz 2, covering the material in Problem Sets 11–23,
is available after class on October 30 Friday.
Applications
 Solving right triangles:
 Reading from the textbook: Section 9.1 (pages 694–696).
 Exercises due on October 26 Monday:
 Answer this in degrees, and also answer it in radians:
If A and B are the two acute angles in a right triangle,
then A + B = ___.
 True or false:
Knowing any two of the three sides of a right triangle
is enough information to solve the triangle completely.
 True or false:
Knowing any two of the three angles of a right triangle
is enough information
to solve the triangle completely.
 Exercises from the textbook due on October 28 Wednesday:
9.1.4, 9.1.11, 9.1.13, 9.1.15, 9.1.17, 9.1.19,
9.1.21, 9.1.23, 9.1.37.
 The Law of Sines:
 Reading from the textbook:
Section 9.2 through Objective 2 (pages 700–704).
 Exercises due on October 28 Wednesday:
In each of the following forms of the Law of Sines,
fill in the blank to get a true theorem
(where a, b and c
are the lengths of the three sides of a triangle
and A, B, and C
are the measures of the respective opposite angles).
 a ÷ sin A =
b ÷ ___.
 b ÷ c =
sin B ÷ ___.
 sin A ÷ a =
sin C ÷ ___.
 Exercises from the textbook due on October 30 Friday:
9.2.9, 9.2.11, 9.2.13, 9.2.15, 9.2.18, 9.2.27,
9.2.29, 9.2.33, 9.2.35, 9.2.37.
 The Law of Cosines:
 Reading from (mostly) the textbook:
 Section 9.3 through Objective 2 (pages 711–713);
 My handout on solving triangles
(DjVu).
 Exercises due on November 2 Monday:
 Which law do you use to solve a triangle,
if you are given two angles and one of the sides?
 Which law do you use if you are given the three sides?
 What do you do if you are given only the angles?
 Exercises from the textbook due on November 4 Wednesday:
9.3.9, 9.3.11, 9.3.13, 9.3.15.
 Area of triangles:
 Reading from the textbook: Section 9.4 (pages 718–720).
 Exercises due on November 4 Wednesday:
 If two sides of a triangle have lengths a and b
and the angle between them has measure C,
then what is the area of the triangle?
 If a triangle's sides have lengths a, b, and c,
then what is the area of the triangle?
(Express this using only a, b, c,
and nontrigonometric operations.
You may use the perimeter or semiperimeter as well, if you find it convenient,
but then you must state what it is
using only a, b, and c.)
 Exercises from the textbook due on November 6 Friday:
9.4.9, 9.4.11, 9.4.13, 9.4.15, 9.4.17, 9.4.19, 9.4.21,
9.4.25, 9.4.27, 9.4.37.
 Applications of solving triangles:
 Reading from the textbook:
 Section 9.2 Objective 3 (pages 704–707);
 Section 9.3 Objective 3 (pages 713&714).
 Exercises due on November 6 Friday:
 If a bearing is N30°E,
then what is the angle that this direction makes with due north,
and what angle does it make with due east?
 If you divide a polygon with n sides into triangles,
how many triangles will you need?
 Exercises from the textbook due on November 9 Monday:
9.2.39, 9.2.49, 9.3.45, 9.3.57, 9.4.46, 9.4.53.
 Harmonic motion:
 Reading from the textbook: Section 9.5 (pages 724–730).
 Exercises due on November 9 Monday:
 Fill in the blank with more than one word:
If the position of an object is a sinusoidal function of time,
then the object is undergoing _________ motion.
 If the sinusoidal function is modified
so that the amplitude is an exponential function with a negative growth rate
(instead of a constant),
then the object is undergoing _________ motion.
 Exercises from the textbook due on November 11 Wednesday:
9.5.7, 9.5.9, 9.5.11, 9.5.13, 9.5.15, 9.5.17,
9.5.19, 9.5.21, 9.5.23, 9.5.25.
 Polar coordinates:
 Reading from the textbook:
Section 10.1 through Objective 3 (pages 740–746).
 Exercises due on November 11 Wednesday:

Fill in the blanks with expressions:
Given a point with polar coordinates (r, θ),
its rectangular coordinates are
(x, y) = (___, ___).
 True or false:
For each point P in the coordinate plane,
for each pair (r, θ) of real numbers
that gives P in polar coordinates,
r ≥ 0 and 0 ≤ θ < 2π.
 True or false:
For each point P in the coordinate plane,
for some pair (r, θ) of real numbers
that gives P in polar coordinates,
r ≥ 0
and 0 ≤ θ < 2π.
 Exercises from the textbook due on November 13 Friday:
10.1.13–20, 10.1.21, 10.1.23, 10.1.25, 10.1.27,
10.1.31, 10.1.33, 10.1.35, 10.1.45, 10.1.47, 10.1.49,
10.1.51, 10.1.53, 10.1.59, 10.1.63.
 Equations in polar coordinates:
 Reading from the textbook:
 Section 10.1 Objective 4 (pages 746&747);
 Section 10.2 through Objective 1 (pages 749–753).
 Exercises due on November 13 Friday:
Let x and y be rectangular coordinates,
and let r and θ be the corresponding polar coordinates.
 Express the following quantities using only x and y:
 r^{2},
 tan θ;
 Express the following quantities
using x, y, and/or r:
 sin θ,
 cos θ.
 Exercises from the textbook due on November 16 Monday:
10.1.77, 10.1.79, 10.1.83, 10.1.85, 10.2.15,
10.2.17, 10.2.19, 10.2.21, 10.2.23.
 Graphing in polar coordinates:
 Reading from the textbook:
The rest of Section 10.2 (pages 753–761).
 Exercises due on November 16 Monday:
 Let a be a positive number,
and consider the circle
given in polar coordinates by
r = 2a sin θ.
The radius of this circle is ___,
and its centre is (___, ___) in rectangular coordinates.
 Let n be a positive integer,
and consider the rose curve
given in polar coordinates by r = sin(nθ).
If n is even, then this rose has ___ petals;
if n is odd, then it has ___ petals.
 Exercises from the textbook due on November 18 Wednesday:
10.2.31–38, 10.2.39, 10.2.43, 10.2.47,
10.2.51, 10.2.55, 10.2.59.
 Complex numbers:
 Reading from the textbook:
Section 10.3 (pages 764–771).
 Exercises due on November 18 Wednesday:
 What is the magnitude (absolute value)
of the complex number x + iy?
 Write the complex number
with magnitude r and argument θ.
 What is the product of
r_{1}(cos θ_{1} + i sin θ_{1})
and
r_{2}(cos θ_{2} + i sin θ_{2})?
 Exercises from the textbook due on November 20 Friday:
10.3.13, 10.3.15, 10.3.17, 10.3.19, 10.3.21, 10.3.23, 10.3.25, 10.3.29,
10.3.33, 10.3.35, 10.3.37, 10.3.41, 10.3.43, 10.3.45, 10.3.47, 10.3.49,
10.3.53, 10.3.55, 10.3.57, 10.3.59, 10.3.61, 10.3.63.
 Vectors:
 Reading from the textbook: Section 10.4 (pages 773–783).
 Exercises due on November 20 Friday:
 Give a formula
for the vector
from the initial point (x_{1}, y_{1})
to the terminal point (x_{2}, y_{2}).
 Give a formula for the magnitude (or norm, or length)
of the vector ⟨a, b⟩.
 Exercises from the textbook due on November 23 Monday:
10.4.11, 10.4.13, 10.4.15, 10.4.17, 10.4.27, 10.4.29, 10.4.37,
10.4.39, 10.4.43, 10.4.45, 10.4.49, 10.4.51.
 Vectors and angles:
 Reading from the textbook: Section 10.5 (pages 788–793).
 Exercises due on November 23 Monday:
 State a formula for
the dot product u ⋅ v of two vectors
using only their lengths u and v,
the angle θ = ∠(u, v) between them,
and realnumber operations.
 State a formula
for the dot product
of ⟨a, b⟩
and ⟨c, d⟩
using only realnumber operations
and the rectangular components
a, b, c, and d.
 Exercises from the textbook due on November 30 Monday:
10.4.61, 10.4.63, 10.4.65, 10.4.67, 10.4.69, 10.5.9, 10.5.11, 10.5.13,
10.5.15, 10.5.17, 10.5.19, 10.5.21, 10.5.23, 10.5.25.
Quiz 3, covering the material above,
is available after class on December 4 Friday.
Quizzes
 Basic trigonometry:
 Review date: September 25 Friday (in class).
 Date due on MyLab: September 28 Monday (before class).
 Corresponding problems sets: 1–10.
 Help allowed:
Your notes, calculator.
(If a question tells you not to use a calculator,
you may still use the calculator to check,
but be sure to give an exact answer.)
 NOT allowed: Textbook, my notes, other people, websites, etc.
 Work to show:
Submit a picture of your work on Canvas,
at least one intermediate step for each result except #3, #7, and #9.
(If a question tells you not to use a calculator,
then be sure that your work
shows how you can solve the problem without using one.)
 Advanced trigonometry:
 Review date: October 30 Friday (in class).
 Date due on MyLab: November 2 Monday (before class).
 Corresponding problems sets: 11–23.
 Help allowed:
Your notes, calculator.
(In graphing problems,
while you may still use a graphing calculator to check,
you should be able to solve the problem without one.)
 NOT allowed: Textbook, my notes, other people, websites, etc.
 Work to show:
Submit a picture of your work on Canvas,
at least one intermediate step for each result except #1.
(In graphing problems,
be sure that your work
shows how you can solve the problem
without using a graphing calculator.)
 Applications:
 Review date: December 4 Friday (in class).
 Date due on MyLab: December 7 Monday (before class).
 Corresponding problems sets: 24–35.
 Help allowed: Your notes, calculator.
 NOT allowed: Textbook, my notes, other people, websites, etc.
 Work to show:
Submit a picture of your work on Canvas,
at least one intermediate step for each result
except #7, #8, and #11.
Final exam
A comprehensive final exam is on December 11 Friday from 10:00 to 11:40.
The exam will consist of questions
similar in style and content
to those in the practice final exam (TBA).
This web page and the files linked from it
were written by Toby Bartels, last edited on 2020 December 3.
Toby reserves no legal rights to them.
The permanent URI of this web page
is
https://tobybartels.name/MATH1200/2020FA/
.