4.0 out of 5 stars
A 1 Hour Review Of Applying Trigonometry To Triangles, August 24, 2010
This review is from: Trigonometry, Part 1 (DVD)
Courses in trigonometry teach both the application of trigonometry to "solve triangles" and also the more general use of trigonometry based on "the unit circle". The DVD "The Standard Deviants, Trigonometry, Vol 1" shows about an hour of material focused on using trigonometry to solve triangles It does not cover trigonometry on "the unit circle" nor does it cover the topics of graphing trig functions and trigonometric identities.
The DVD does not drill you in the material. It works only one or two example problems to illustrate each concept. The lessons are weak on explaining the "why" of the material. Topics such as the the law of sines and the relation between degrees and radians are merely presented as facts to be memorized. The lessons are strong on giving hints to aid rote memorization. For example, you are taught to use the phrase "soh cah toa" (accompanied by scene of people soaking their toes) to remember the definitions of sine, cosine and tangent.
Apparently the video was originally a VHS tape, copyrighted 1997. The title is actually "The Twisted World Of Trigonometry, Part 1". The quality of the video is good. It is a professional production. There are ample computer generated graphics. The features in the diagrams change color to indicate what the narrator is talking about. The video twice refers to a "reader insert card". I didn't find such a card with the DVD. The card apparently contains a few facts that can also be found textbooks.
A troup of actors called "The Standard Deviants" performs this video. Academic material is mixed with momentary, nonsensical and somewhat humorous skits, all G-rated stuff.
I give this DVD four stars out of five to indicate that it is an effective "cram school" review of trigonometry applied to triangles. I'm not penalizing it for failing to providing a genuine understanding of the material or for not presenting repetitive drills.
I notice that the publisher of this DVD, Cerebellum Corporation, also sells other trigonometry DVDs whose titles suggest that they might be the individual parts of "The Twisted World Of Trigonometry: Part 1". If anyone knows the facts of this matter, I hope they will add a comment to this review and tell us because I don't intend to buy them just to find out.
Synopsis
Part 1
Part 1 Section A Terms
Definitions of ray,vertex,initial side,terminal side, angle
Angles are illustrated by the hands of a clock.
The measurement of angles is explained.
Definition of an angle on a cartesian coodinates graph in "standard position"
Definition of a "quadrantal angles"
Definition of quandrants, I, II, III, IV.
Part 1 Section B Degree and Radian Measurement
A full circle = 360 deg.
Defintion of a right angle
Definition of a straight angle
Radians aren't defined. The fact that "one revolution equals 2 pi radians" is asserted.
Examples of how to convert degrees into radians and vice versa:
Convert 120 deg to radians
Convert (11 pi)/12 to degrees
The "special angles" are briefly mentioned.
Part 2 Right Triangle Trigonometry
Definition of triangle
Right triangle
Acute angles
Legs of a right triangle
hypotenuse
Part 2 Section A The Pythagorean Theorem
Example find hypotenuse of right triangle that has legs of lengths 3 and 4
Part 2 Section B Six Trig Functions
Defines the six trig functions as ratios of sides in a right triangle
Example: Find the values of the trig function of the angle alpha, opposite to a side of length 3 in a 3,4,5 right triangle.
The reciprocal relationships of pairs of trig functions
Sum of angles in a triangle is 180 deg = pi radians
Definition of complementary angles
Remarks about "cofunctions"
Any trig function of an acute angle = the cofunction of its complementary angle
Find all trig functions of an angle alpha whose sine is 5/6
Use the mnemonic "soh cah toa" to remember the ratios that define the sine,cosine and tangent.
Part 2 Section C Trigonometric Values
A table of trig values of the "special angles" is shown. The viewer is advised to memorized it.
The DVD does not derive or dwell on this table and only makes use of it a few times.
[The significance of the trig values of "the special" angles may be gradually waning in math and science education. In pre-calculator days, teachers needed to design problems where the answers had some simple form and using the special angles (30 deg, 45 deg, 60 deg) in problems was the convenient way to do this. This was true not only in trig courses, but also in calculus, physics etc. The trig functions of the special angles can be found by analyzing analyzing an equilateral triangle with an altitude drawn in it and a square with a diagonal drawn. When the focus is on understanding mathematics, doing this analysis can reinforce the definitions of the trig functions. However, this DVD and most "cram school" approaches merely present the trig functions of these angles as a table to be memorized. Problems involving the special angles are probably still prominent in many tests. If you are preparing to be tested, then you should look for additional materials that drill you in such problems.]
Using calculator to find trig functions is explained. On some calculators you find inverse trig functions by using the "inv" key with the key for the function. You must be careful to have the calculator in the correct mode, degrees mode vs radian mode.
Example: find the inverese sine 0f .813
(The DVD takes for granted that the viewer understands the concept of "inverse functions". It assumes the viewer already understands the meaning of terminology like "inverse sine".)
Using inverse trig functions to find the angles in the previous example of a 5, sqrt(11), 6 right triangle.
Part 2 Section D Solving Right Triangles
To "solve" a triangle means to find all the sides and angles from the given information.
Right triangles are solvable given two sides, or a side and an acute angle
Example: acute angle 45, adjacent side = 5
Example: hypotenuse = 8, side 'a' = 4
Bigger sides have bigger angles opposite them
Example: Use the above fact to check the solution of the previous example
Part 3 Oblique Triangles
An oblique triangle is a triangle that has no right angle
The two types of oblique triangles: 3 acute angles, 2 acute angles and one obtuse
Explains terminology and abbreviations such as "SAA", "side,angle,angle".
The cases where a triangle can be "solved" are:
1. SAA
2. ASA
3. SSA
4. SSS
5. SAS
Part 3 Section A Law of Sines,
Use the Law Of Sines to solve the cases where the angle is named last.
For SAA,ASA,SSA, use the Law of Sines; note the last given value is 'A', an angle.
Use the Law of Cosines to solve the cases where the side is named last.
For SSS,SAS, use the law of cosines; note last known value is 'S', a side
(Those are fine rules if you remember to write "SAA" instead of "AAS".)
The Law of Sines is stated, assuming the standardized labeling of a triangle used by the DVD, side 'a' is opposite angle alpha etc.
Example: Solve the ASA case given 45 deg, 2, 73 deg
The example shows a calculator being used.
The case SSA may produce ambiguous answers. The DVD warns about this but doesn't explain why. The viewer is told to consult a textbook for the details.
Part 3 Section B The Law Of Cosines
The Law Of Cosines is stated, assuming the standardized labeling of a triangle
Example: Solve the SAS case given 2, 50 deg, 5
You can use law of sines to check answers.
Hints are given about how to remember the laws, using the standardized labeling.
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