- Textbook access (DjVu instructions).

- General review:
- Reading from the textbook: Section 2.1 (pages 150–153).
- Exercises due August 29 Thursday:
- 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 September 3 Tuesday on MyLab: 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 September 3 Tuesday:
- 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 September 5 Thursday on MyLab: 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 (pages 518–526).
- Exercises due September 5 Thursday:
- 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°?
- Fill in the blank with an algebraic expression:
In a circle of radius
*r*, a central angle whose measure is*θ*radians subtends an arc whose length is*s*= ___.

- Exercises from the textbook due September 10 Tuesday on MyLab: 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, 7.1.71, 7.1.73.

- Right triangles:
- Reading from the textbook: Section 7.2 (pages 531–538).
- Exercises due September 10 Tuesday:
- 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 September 12 Thursday on MyLab: 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 September 12 Thursday: 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.)
- Exercises from the textbook due September 17 Tuesday on MyLab: 7.3.7, 7.3.19, 7.3.21, 7.3.32, 7.3.27, 7.3.29.

- General angles:
- Reading from the textbook:
- The rest of Section 7.3 (pages 546–549);
- Section 7.4 through Objective 5 (pages 555–561).

- Exercises due September 17 Tuesday:
- 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 September 19 Thursday on MyLab: 7.3.31, 7.3.33, 7.3.35, 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.

- Reading from the textbook:
- 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 September 19 Thursday:
- 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 September 24 Tuesday on MyLab: 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 September 24 Tuesday:
- 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 September 26 Thursday on MyLab: 7.5.63, 7.5.65, 7.5.69, 7.5.81, 7.5.85, 7.5.87, 7.6.3.

- Basic graphing:
- 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);
- 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 September 26 Thursday:
- What are the intercepts of the graphs of the sine and tangent functions?
- What are the intercepts of the graph of the cotangent function?
- Besides the answers to (2) above, what additional intercept does the graph of the cosine function have?
- What is the intercept of the graph of the secant function?
- What are the asymptotes to the graphs of the tangent and secant functions?
- What are the asymptotes to the graphs of the cotangent and cosecant functions?

- Exercises from the textbook due October 3 Thursday on MyLab: 7.6.6, 7.6.8, 7.6.11, 7.6.13, 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:
- Transformations of trigonometric functions:
- Reading from the textbook:
*Skim*: Section 3.5 (pages 254–263);- 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 October 3 Thursday:
- To get the graph of
*y*= −*f*(*x*) from the graph of*y*=*f*(*x*), which axis do you reflect the graph across? - To get the graph of
*y*= 2*f*(*x*) from the graph of*y*=*f*(*x*), do you*stretch*the graph vertically or*compress*it? - To get the graph of
*y*=*f*(2*x*) from the graph of*y*=*f*(*x*), do you*stretch*the graph horizontally or*compress*it?

- To get the graph of
- Exercises from the textbook due October 8 Tuesday on MyLab: 3.5.41, 3.5.35, 3.5.45, 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 8 Tuesday:
- 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 October 10 Thursday on MyLab: 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 (mostly) the textbook:
- Section 8.1 (pages 622–631);
- Section 8.2 (pages 635–638);
- My handout on inverse trigonometric operations (DjVu).

- Exercises due October 10 Thursday:
Fill in all of these blanks with algebraic expressions
(most of which will be constants):
- 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*≤ ___. - cos sin
^{−1}*x*= ___ (if either side exists).

- That
- Exercises from the textbook due October 15 Tuesday on MyLab: 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, 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 and related formulas:
- Reading from the textbook:
- Section 8.5 Subsections 1–3 (pages 659–666);
- Section 8.6 through Example 2 in Subsection 2 (pages 672&674).

- Exercises due October 15 Tuesday:
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 October 17 Thursday on MyLab: 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, 8.5.83, 8.5.85.

- Reading from the textbook:
- Half-angle and related formulas:
- Reading from the textbook:
- The rest of Section 8.6 Subsection 2 through Example 3 (pages 674&675);
- Section 8.6 Subsection 3 (pages 676–678);
*Optional*: Section 8.7 (pages 683–685).

- Exercises due October 17 Thursday:
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 October 24 Thursday on MyLab: 8.6.9, 8.6.11, 8.6.13, 8.6.15, 8.6.17, 8.6.19, 8.6.25, 8.6.29, 8.6.23, 8.6.27.

- Reading from the textbook:
- Simplifying trigonometric expressions:
- Reading from (mostly) the textbook:
- My handout on simplifying trigonometric expressions (DjVu);
- Section 8.4 (pages 651–656).

- Exercises due October 24 Thursday:
- 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 October 29 Tuesday on MyLab: 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);
- Section 8.5 Subsection 4 (pages 666–668);
- Section 8.6 Subsection 2 Examples 4&5 (pages 675&676).

- Exercises due October 29 Tuesday:
- 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*. (Hint: 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 October 31 Thursday on MyLab: 8.3.13, 8.3.23, 8.3.25, 8.3.27, 8.3.37, 8.3.39, 8.3.61, 8.3.73, 8.3.109, 8.3.115.

- Reading from the textbook:

- Solving right triangles:
- Reading from the textbook: Section 9.1 (pages 694–696).
- Exercises due October 31 Thursday:
- 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 November 7 Thursday on MyLab: 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 (pages 700–706).
- Exercises due November 7 Thursday:
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 November 12 Tuesday on MyLab: 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 (pages 711–714);
- My handout on solving triangles (DjVu).

- Exercises due November 12 Tuesday:
- 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 November 14 Thursday on MyLab: 9.3.9, 9.3.11, 9.3.13, 9.3.15, 9.2.39, 9.3.45.

- Reading from (mostly) the textbook:
- Area of triangles:
- Reading from the textbook: Section 9.4 (pages 718–720).
- Exercises due November 14 Thursday:
- 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*non*-trigonometric 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*.)

- If two sides of a triangle have lengths
- Exercises from the textbook due November 19 Tuesday on MyLab: 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, 9.4.43, 9.4.53.

- More to come!

Go back to the the course homepage.

This web page was written by Toby Bartels, last edited on 2019 October 28. Toby reserves no legal rights to it.

The permanent URI of this web page
is
`http://tobybartels.name/MATH-1200/2019FA/homework/`

.