Tests and quizzes will be announced in class
along with the point value of each in accordance with the progress made
in
class. Frequently the class will vote
on options for testing presented. On the day of the decision
the date, material covered and point value of the test or quiz will
be posted. The test or quiz will be graded and returned the next
class day. The tests will reflect the homework assignment and
the work presented in class and will not be curved. In addition to
the tests and quizzes given, points will be given and taken for homework,
presentations and contributions made during class. At the end of
the quarter the sum of the points earned during class, be that a positive
or negative number will be added to the sum of the test / quiz scores.
This number will then be divided by the total number of points possible
on the test / quizzes. The letter grades for the report card will
be determined by the grading system of Salesianum School which can be in the
student hanbook.
There will be a final project which will involve math learned throughout his entire education. A weeks worth of in class activity will be devoted to it. In addition to the project there will be a final exam. As of the beginning of the semester every student in the class will be exempt from the final. A student will lose that exemption by any of the following choices he makes:
1. Being rude in class to either the teacher or fellow classmates
2. Sleeping in class often
3. Not doing the work on
the project during the class time provided
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8/28/08 9/2/08 9/3/08 9/5/08 9/7/08 9/9/08
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9/17/08
9/21/08 2/8/08
2/11/08 2/12/08 2/13/08 2/15/08 2/19/08 2/20/08
2/22 -23/08
2/27/08 2/28/08
2/29/08
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3/19-30/08
3/31/08
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4/9-10/08
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p. 7, 40 - 58 and p.8, 61 - 68 p.7, 23 - 41 odd p.8 69-74 all
p.8, 69-74 draw the angle and find the 6 functions of each angle
50 pt Quiz on the 6 trig functions, Degree measure Sec.3 has the quiz 6th pd. Thursday Sec 4 has it 2nd pd Friday
p.24 1-12p.25, 17-24,
p.34, 27-34, p.35, 55-62 p.35, 64 - 71
Sum and Difference Formulas for Sine and Cosine (see notes) Homework will be a hand out. (FFAWS) Handout Worksheet 2
Both sections will have the quiz when we get back on Tuesday 50 pt Quiz sec 3 Quiz back, start right triangle trig. HW p.73-74, 9 - 29 odd pp.74 - 76 35- 45 odd Traveling toward the mountain problem and the airplane landing problem
The surveyor on a hill, the airplane runway, and the approaching a mountain problems Practice quiz for rt. triangle trig. Real quiz on solving rt. triangles
Finish handout given on Monday
Sum and Difference formulas for Sine and Cosine See your notebook for the sines and cosines of the special angles 30 45 60 120 135 150 210 225 240 300 315 330
Quiz back, start radian measure.
Do pp.98 - 99, 1-54
p.98 #57 - 74 We will do #75 in class sec. 4
We will do #75 in class sec. 3
Quiz 2 30 pts 2 problems draw the triangle and solve it. given a side and an acute angle of a right triangle or given 2 sides of a right triangle, find the remaining side and the acute angles Begin radian measure Read pp. 94 - 96 and do 1 - 73 odd on pp 97,98 In class project on paper graph. Due at end of class I Discussion of the graph of y= a sin(bx) +d
Holiday Welcome back! Finish Graph project. Intro. to the sinusoidal functions.
Handout homework (practice quiz)
Real Quiz 50 pts.
Start graphing in radian mode.
"Going Backwards"
Quiz back and start Law of Sines Law of Cosines
When asked to graph "over 2p", the Xmax will be 2p and you will see and graph b waves. When asked to graph "over 2 or 3 cycles", the Xmax will be the number of cycles time the period, 2p/b and you will see and graph the . number of waves.
Working with sinusoidal functions in both degrees and radians. y = a sin(bx + c) + d
Working with sinusoidal functions with phase shift now included
Phase Shift = -c/b The Xmin will now be the phase shift and the Xmax will be: Xmin + 360 for over 360 Xmin + 2p for over 2p Xmin + n times the period for over n cycles
You will find the Law of Sines on pp.276 - 286 You will find the Law of Coines on pp.293 - 300 Last Quiz of 2008 (20 pts.) Hand out final project All class days until Thursday 5/22/08 The Final Assessment Project will count as 20% of your grade for the course.
End of Trigonometry 441 Final exam will be only for uncooperative students at 9Am in Room A206
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Notes
Introduction to the class - rules procedures, etc. Introduction to angles in Trigonometry Any real number can be represented as an angle. Be able to draw any angle and find 2 angles coterminal to it, one positive, one negative whose measure is between -360 and 360.
The instructions fro problems 69 - 74 were given in class. Draw the angle. Find the 6 trig functions and the angle. sine = y/r cosine = x/r tangent = y/x cosecant = r/y secant = r/x cotangent = x/y To get r: use x2+ y2 = r2 To get the reference angle: 1. Check the mode. It should be in degrees 2. press 2nd and then your choice of sin, cos, or tan. 3. Then enter the positive of the y/r, x/r, or y/x To get the angle: 1. In the first quadrant, do nothing the reference angle is the angle 2. In the second quadrant, subtract the reference angle from 180. 3. In the 3rd quadrant, add 180 to the reference angle. 4. In the 4th quadrant, subtract the reference angle from 360. The only Pythagorean Triples I will use are: 3-4-5, 5-12-13, 8-15-17, and 7-24-25
Find the quadrant: I II III or IV
The largest number in each triple is the hypotenuse, r, and will always be positive. The other two numbers are either x or y and they can be either positive or negative depending on which quadrant the angle is in. sin(A + B) = sinAcosB + cosAsinB sin(A - B) = sinAcosB - cosAsinB cos(A + B) = cosAcosB - sinAsinB cos(A - B) = cosAcosB + sinAsinB
Quiz will cover drawing and labeling right triangles and the application problems demonstrated in class. Remember: one of the sides of an angle of elevation or depression is horizontal Find all of the other 5 trig functions after finding the reference angle, then finding and storing the actual angle Reciprocal Functions Practice Drawing and solving right triangles. Angles of depression and elevation Surveying problems - the height of a tree on a hill Applications: the runway problem - p. 83 #26 approaching the mountain - p. 83 #23 - 25 Quiz on applications of right triangle trigonometry
The circle chart of # 75 is very important to future work
There will be a quiz on the "special triangles" and their relation to trigonometry. The directions will read, "Draw the angle and the reference triangle. Find the 6 trig ratios of the the angle in simplest fraction radical form." Find all 6 trig functions of the special angles in simpl,est radical form From a point on the terminal side draw to the x axis NOT to the y axis. Show all units in numerators and denominators. Degrees to radians x p/108 Radians to degrees x 180/ p Arc length = radius x angle (in radians) Linear velocity = angular velocity x radius Just get them into the right units and multiply. ______________________________________________________________________________________ Sinusoidal Equations y=a sin (bx) +d or y=a cos (bx) +d |a| = amplitude, d = middle, d + |a| = top, d - |a| = bottom b = frequency, the number of complete waves in 360 degrees 360/b = period, the length of each complete wave When asked for one cycle of the function this is your Xmax. When asked to graph "over 360", the Xmax will be 360 and you will see and graph b waves. Homework for weekend 4/4 - 4/6 1.) y = 5sin (3x) - 2 over 360 degrees, in degrees, find 2nd root 2.) y = -100cos (45x) + 25 over one cycle, in degrees, find last root 3.) y = .2 cos (2x) - .05 over 360 degrees, in degrees, find 3rd root 4.) y = -3000sin (.06x) +900 over one cycle, in degrees, find 1st root Don't worry about the phase shift (horizontal shift). I'll teach that later. You can copy and print this if you run out of papers that I gave you in class. Xmin = _____ Equation______________ in ____ over _____
amplitude = ____ frequency = ____ period = ____
Xmax = _____ middle (vertical shift) = ______
Xscl = _____ top = ___ bottom = ____
Ymin = _____ phase shift (horizontal shift) = ______ end of wave(s) =___
Ymax = _____
Yscl = _____
__________________________________
Everything is the same as for degrees except that to find the period divide 2p by the frequency instead of 360. Also make sure you put the calculator in radian mode before you hit graph.
Going Backwards Top, middle, and bottom lie on tick marks.
amplitude = ____ frequency = ____ period = ____
middle (vertical shift) = ______ top = ___ bottom = ____
Y1 = _________________ Y2 =______ Y3 = ญญญญญญ______ Y4 = ______
amplitude = ____ frequency = ____ period = ____
middle (vertical shift) = ______ top = ___ bottom = ____
Y1 = _________________ Y2 =______ Y3 = ญญญญญญ______ Y4 = ______
amplitude = ____ frequency = ____ period = ____
middle (vertical shift) = ______ top = ___ bottom = ____
Y1 = _________________ Y2 =______ Y3 = ญญญญญญ______ Y4 = ______
amplitude = ____ frequency = ____ period = ____
middle (vertical shift) = ______ top = ___ bottom = ____
Y1 = _________________ Y2 =______ Y3 = ญญญญญญ______ Y4 = ______
The handout will tell you what to do. Take notes on why you are doing it. The project result will be worth 10 pts. and there will be a 30 pt. quiz on the "why" part.
Real Quiz (50 pts.) Graph 4 functions in both degrees and radians. over 360 or 2p and over a given number of cycles.
y = sin x y = cos x Homework for 12/03/07 1.) y = 2.5cos(3x) - 12, over 2p in radians find 2nd root 2.) y = 4000sin(314x) + 1500 , over 1 cycle in radians find first root 3.) y = .048cos(.023x) - .012, over one cycle in radians find last root 4.) y = -30sin(.06x) – 8, over 2 cycles in degrees find 1st root
sec.2 answer only items a, d, e, f, and h and the window NOT over ____ and in ______. 1.) y = 25cos(x) - 12, find 2nd root 2.) y = -150sin(x) + 40 , find first root 3.) y = .012cos(x) - .004, find last root 4.) y = 30sin(x) + 12, find 1st root Homework for 5/6/07 1.) y = 2.5cos(3x - 90) - 12, over 360 in degrees find 2nd root 2.) y = 4000sin(60x + 120) + 1500 , over 1 cycle in degrees find first root 3.) y = .048cos(2x - 80) - .012, over 2p in radians find last root 4.) y = -30sin(.02x + 1) – 8, over 2 cycles in radians find 1st root Homework: pp.282 - 283, 5-21 odd Homework: pp.291- 292- 5-21 odd
5/5/07 Handout - This handout will model the last 50 pt. quiz exactly 1/9, 10/07 Practice quiz on Sum and difference formulas 5/10,11/07 Last 50 pt. quiz 5/12/07 Quiz back Laws of Sines and Cosines Week of 5/16 - 19 You will receive a 20 pt take home quiz on law of sines and cosines. "When you turn it in you will receive the 100 pt. project which will count as the final exam.. The latest the time project will be accepted is 3 PM on Friday the 19th.
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