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T
3/1/05
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HW due:
Set up 2 trigonometry problems and process them through all 5 departments (Sketch,
Equation, Algebra, Calculation, and Quality Assurance). If you do not have a
scientific calculator, you may use the table on p. 424 when you reach the
Calculation Dept. Label your steps S, E, A, C, and QA, and be sure that the
result of the Algebra step does not contain any decimal approximations. For
example, your Algebra step could be something like x = 25 sin 36°, but you would not write x » 25(.5878) until you reach the Calculation Dept.
Important:
For at least one of the problems, make the unknown be an angle. If you did
not have a chance to serve in the Calculation Dept. on Friday, you will have
to read the “crash course” below to see how to do this.
“Crash
Course” Example: Let 7 cm and 12 cm be the lengths of the legs of a
right triangle. Compute the smaller angle.
Solution:
The smaller angle is opposite the leg of length 7 cm. Call this angle q (the Greek letter theta is commonly used in
problems of this type).
S: [You have to make the sketch yourself.]
E: tan q = 7/12
A: q = tan–1
(7/12)
C: q » 30°15' by calc.
QA: By Pythag. Thm., the hypotenuse is Ö193, which is a little less than 14. (Since we know
all our perfect squares through 252, we know that 142 =
196.) Thus sin q » .5 since
opposite/hypotenuse » 7/14. Or, to put it another way, we have a short leg that is just
about half as long as the hypotenuse. That means that the D must be nearly in the 30°-60°-90° family, with q » 30°. APPROVED.
Explanation:
The tan–1 function (inverse tangent) used in the “A” step is the
tricky part. We read this equation as, “Theta equals the angle whose tangent
is 7/12.” In other words, the inverse tangent is like the reverse of finding
a tangent. If you do not have a fancy scientific calculator with a tan–1
key, you can simulate the process by looking in the tangent column of the
table on p. 424. The decimal value of 7/12 is approximately .5833. Scan down
the tangent column until you find the value that is closest to .5833; do you
see that it’s about 30°?
Here are some more examples:
1. If sin ŠA = 14/17, what is ŠA?
Solution: ŠA = sin–1
(14/17) » sin–1
(.8235) » 55° by the table on p. 424.
If you have a scientific calculator, you can punch in sin–1
(.8235) and get 55°26' immediately.
2. If cos ŠQ = 13.2/19, what is ŠQ?
Solution: ŠQ = cos–1
(13.2/19) » cos–1
(.6947) » 46° by the table on p. 424.
3. If the legs of a right D are in a 5:1 ratio, find all the angles.
Solution: Obviously, one of the angles is 90°. The challenge is to find the others. The smallest angle,
which we will call a (Greek letter alpha), is opposite the short leg. Make a diagram to
show that tan a = 1/5. Therefore, a = tan–1 (1/5) = tan–1 0.2 » 11° by the table on p. 424. The remaining angle must be the complement,
namely 79°. These answers are
acceptable approximations; if you wanted more accurate results, you would
need to use a scientific calculator or perform what is called “interpolation”
on the table on p. 424.
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W
3/2/05
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HW due:
Read p. 441; write §10.1 #4, 5, 7, 11-15 all, 17.
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Th
3/3/05
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HW due:
Finish your §10.1 problems, filling in all the placeholders you may have
previously created. Use the diagram given at the end of class yesterday as a
starting point for #14. This assignment should now be complete.
Trigonometry Quiz (10 pts.): You
will be given a pair of word problems similar to #9 or #10 on p. 426. You
will be required to process the problems through all “departments” except for
using the calculator. In other words, you must perform the sketch, equation,
algebra, and QA estimate. You will leave your answer in a form that could be
handed to a calculator operator. At the end, I may ask you to punch the
buttons to obtain an answer. Time limit: 5 minutes (7½ minutes for extended
time). I may be generous and provide 10 minutes (double time) for everyone.
However, when time is up, time is up.
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F
3/4/05
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HW due:
Read §10.2; write §10.2 #1, 2, 4, 6, 13. Also, remember that you will need to
have a clean copy of §10.1 #13 available to hand in.
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M 3/7/05
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HW due:
Choose a selection of review problems from Chapter 9 and 10. Show your work
and keep a time log of at least 35 minutes. If you are not comfortable
selecting your own problems, here are some suggestions:
p. 426 #6 (requires calculator), 10, 11, 15
p. 431 #20 with the following modification: answer (a) and (b) for arc RT
instead of arc RTC
p. 505 #4ab
p. 506 #7ab, 10, 12
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T
3/8/05
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Test on §§9.7–10.2.
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W
3/9/05
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HW due: Read §§10.3, 10.4; write §10.3 #1-4 all, 7, 12, 16,
20.
Note: Problem #16 is very short if you use auxiliary segments AE and
CE. Also, #20 is very short if you use #16 as a lemma.
In class: Big Trig warmup.
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Th
3/10/05
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HW due: Write §10.4 #13ab, 27. Hint for #27: Find
length BC, and then work with a pair of similar triangles.
In class: We will try to cover all the HW in §§10.3 and 10.4 today.
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F
3/11/05
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HW due: §10.5 #1-15 all (no need to copy diagrams).
In class: Angle-arc puzzles
with substitute teacher. Sharing ideas in small groups is OK, but each
student must submit his own work on Monday.
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M
3/14/05
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HW due: Angle-arc puzzles from last Friday.
Optional: If you desire additional problems, try these or make up some of your own!
It’s quite a bit of fun.
The BIG TRIG CHALLENGE in Room S
(originally scheduled for today, in celebration of Pi Day) has been postponed
because of a meeting. Because there are also meetings Tuesday, Wednesday, and
Thursday after school, rescheduling may be difficult. However, stay tuned for
more information.
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T
3/15/05
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Bonus HW due today (as announced in class): Make up your own angle-arc puzzle. If it is
original and worthy, it will be posted on geometryquest.com.
If you have a chance, please work the following problems before class: §10.6
#1, 2, 4, 5, 7, 8. If you do not, I cannot penalize you, since they were not
posted by a reasonable time.
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W
3/16/05
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HW due:
Write §10.6 #1, 2, 4, 5, 7, 8; §10.7 #9, 11, 17, 19. Hint for #11: Read the sample problem at the top of p. 463.
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Th
3/17/05
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HW due:
(A period) Write §11.2 #1-9 all, 14, 15, and try #22.
(E and F periods) Write §10.7 #25, §10.8 #1-5 all, 8, 9, 13.
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F
3/18/05
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HW due:
(A period) Write §11.3 #1, 2, 3, 6, 7, 11, 13, 17.
(E and F periods) Write §10.9 #3, 4, 5, 9, 10, 16, 17.
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Week
of 3/21/05
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No school.
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Week
of 3/28/05
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No school.
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