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: 928-6157-2182.
- Final exam time: December 11 Friday from 10:00 to 11:40 in ESQ 100D.

- Name: Toby Bartels, PhD.
- Canvas messages.
- Email: TBartels@Southeast.edu.
- Voice mail: 1-402-323-3452.
- Text messages: 1-402-805-3021.
- Virtual office hours:
- Mondays and Wednesdays from 1:00 PM to 2:00,
- Tuesdays and Thursdays from 10:30 to 12:00, and
- by appointment.

- 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*= ___.

- In a circle of radius
- 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?

- Fill in the blank:
The sine of the complement of
- 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 non-unit 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*.

- 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
- 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.

- Reading from the textbook:
- 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.

- 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.

- Reading from the textbook:
- 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).

- Section 7.7
through
"The Graph of the Cotangent Function
- 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.

- Reading from the textbook:
- Coordinate transformations:
- Review from (mostly) the textbook:
- Section 3.5 (pages 254–263);
- My online notes on linear coordinate transformations.

- Exercises due on September 28 Monday:
Assume that the axes are oriented in the usual way
(positive
*x*-axis to the right, positive*y*-axis 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*(2*x*), do you*compress*or*stretch*the graph left and right?

- Fill in the blank with a direction:
To change the graph of
- 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.

- Review from (mostly) the textbook:
- 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*(2*x*)? - What is the period of 2
*f*(*x*)?

- What is the period (as a function of
- 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.

- Reading from the textbook:
- 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(*ω**x*) 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(*ω**x*−*φ*) for all*x*, with 0 ≤*φ*< 2π, then what is the phase shift of*f*?

- If
- 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.

- Reading from (mostly) the textbook:
- Inverse trigonometric operations:
- Reading from the textbook:
- Section 8.1 through subsection 7 (pages 622–630);
- Section 8.2 through subsection 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*≤ ___.

- That
- 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.

- Reading from the textbook:
- More inverse trigonometric operations:
- Reading from (mostly) the textbook:
- The rest of Section 8.1 (pages 630&631).
- The rest of Section 8.2 (pages 637&638);
- My handout on inverse trigonometric operations (DjVu).

- 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.)

- cos sin
- 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.

- Reading from (mostly) the textbook:
- Sum-angle 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*) = ___.

- sin(
- 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.

- Double-angle 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(2
*α*) using sin*α*and/or cos*α*. - Express sin
^{2}*α*using sin(2*α*) and/or cos(2*α*). - 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.

- Express sin(2
- 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.

- Reading from the textbook:
- Half-angle 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).

- sin
- 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:
- My handout on simplifying trigonometric expressions (DjVu);
- Section 8.4 (pages 651–656).

- 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*?

- Fill in the blank with an expression
in which sin
- 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.

- Reading from (mostly) the textbook:
- 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 3*θ*belong to?

- Write a general form
for the solutions of tan
- 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*+*x**y*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 sum-angle formula, what should you multiply both sides of the equation by? - To solve
sin (
*a**θ*) + sin (*b**θ*) = 0, how can you factor the left-hand side?

- Since you can factor
- 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.

- Reading from the textbook:

- 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.

- Answer this in degrees, and also answer it in radians:
If
- 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.

- To come.

- 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 #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.
- NOT allowed: Textbook, my notes, other people, websites, etc.
- Work to show: TBA.

- Applications:
- Review date: December 4 Friday (in class).
- Date due on MyLab: December 7 Monday (before class).
- Corresponding problems sets: TBA.
- Help allowed: Your notes, calculator.
- NOT allowed: Textbook, my notes, other people, websites, etc.
- Work to show: TBA.

This web page and the files linked from it were written by Toby Bartels, last edited on 2020 October 21. Toby reserves no legal rights to them.

The permanent URI of this web page
is
`http://tobybartels.name/MATH-1200/2020FA/`

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