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The Trigonometry and Pre-Calculus Tutor Set! - 5 Hour Course!
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Product Description
Product Description
The Trigonometry and Pre-Calculus Tutor is the easiest way to improve your grades in Trig and Pre-Calculus! How does a baby learn to speak? By being immersed in everyday conversation. What is the best way to learn Trig and Pre-Calculus? By being immersed in it! During this course the instructor will work out hundreds of examples with each step fully narrated so no one gets lost! Most other DVDs on Trig and Pre-Calculus are 2 hours in length. This DVD set is over double the running time and costs much less! See why thousands have discovered that the easiest way to learn Trig and Pre-Calculus is to learn by examples!
From the Contributor
I have tutored many, many people in Math through Calculus, and I have found that if you start off with the basics and take things one step at a time - anyone can learn complex Math topics. This 2-DVD set contains 5 hours of fully worked example problems in Trig and Pre-Calculus.
After viewing this DVD course in Trigonometry and Pre-Calculus you'll discover that the material isn't hard at all if it is presented in a clear manner. No knowledge is assumed on the part of the student. Each example builds in complexity so before you know it you'll be working the 'tough' problems with ease!
Have a problem with your homework? Simply find a similar problem fully worked out on the Trigonometry and Pre-Calculus Tutor 2-DVD set!
Topics Covered:
Disk 1
Section 1: Complex Numbers
Section 2: Exponential Functions
Section 3: Logarithmic Functions
Section 4: Solving Exponential and Logarithmic Equations
Section 5: Angles
Disk 2
Section 6: Finding Trig Functions Using Triangles
Section 7: Finding Trig Functions Using The Unit Circle
Section 8: Graphing Trig Functions
Section 9: Trig Identities
About the Actor
The author has a BS and MS in Electrical Engineering and an MS in Physics.
Other Titles Available By This Author: The Math Video Tutor - Fractions Thru Algebra - 10 Hour Course!
The Algebra 2 Tutor - 6 Hour Course!
Product details
- MPAA rating : Unrated (Not Rated)
- Product Dimensions : 7.5 x 5.5 x 0.5 inches; 4.8 ounces
- Director : Jason Gibson
- Media Format : Multiple Formats, Color, Closed-captioned, Full Screen, NTSC
- Run time : 5 hours
- Release date : October 25, 2005
- Actors : Jason Gibson
- Studio : Tapeworm Video
- ASIN : B000B51SRI
- Country of Origin : USA
- Number of discs : 2
- Best Sellers Rank: #129,133 in Movies & TV (See Top 100 in Movies & TV)
- #5,608 in Special Interests (Movies & TV)
- #9,549 in Kids & Family DVDs
- Customer Reviews:
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The instructor is great pointing out every step in the solution. I wish I had this crutch when I took Trig. A great buy and sure to work specially if you, like myself, do not have a natural ability in mathematics.
One major caveat. Significant aspects of pre-calc are not mentioned in this set. So don't think that just by reviewing this set you will be ready for calculus. Not by a long shot.
I am looking forward to getting into the "Calculus Tutor" set by the same instructor.
The entire video uses one camera angle, which shows Jason working at the marker board. There are no fancy computer graphics to illustrate mathematical ideas. Jason is well prepared. He speaks clearly. His presentation is spontaneous. It is also very organized and smooth. He has the habit of saying "OK?" every few seconds, but even good lecturers have their idiosyncrasies. You can see his work clearly; he doesn't stand in front of what he is writing. He erases problems quickly after he finishes, but you can use the "pause" function on the DVD player to take a longer look.
Jason doesn't solve any problems that require finding the unknown sides of a triangle using trigonometry on these DVDs He doesn't cover the Law Of Sines or the Law Of Cosines. He doesn't cover the trigonometric form of complex numbers. When trigonometry or pre-calculus is taught in college, the course usually requires the use of a sophisticated calculator. These DVDs have no examples of using one. (Jason does have another DVD that covers the TI-84, which I have not yet watched.)
Accepting the limited scope of the material, I rate this set of DVDs as four stars out of five to indicate that is an excellent set of marker board lectures on rote problems. Understanding only these problems won't get you an A+. However, if you don't know this material, you'll have a hard time passing.
Synopsis
( I use the customary notation "x^p" to mean "x raised to the p power".)
Disk 1
1) Complex Numbers ( about 40 minutes )
He considers the equation x^2 = -25 and shows how it can be given a solution by defining
i = square roof of (-1).
Thet three types of numbers are: real, imaginary, complex.
He explains a graph of the complex plane. (He doesn't make any further use of the graph.)
He explains how to add complex numbers.
Simplify (3 + 2 i) + (-5 + 4i).
Simplify 7 - (3 - 7i).
He explains the multiplication of complex numbers.
Simplify ( 4 + 3i)(-1 + 2i).
Simplify -9i(4-8i).
Simplify 1/(3 + 2i).
Jason says "Mathematicians don't like to have square roots in the denominator. Well,they don't like to have imaginary numbers in the denominator either." (That's a slander on mathematicians. It's educators and graders who don't like this. They want everyone in class to get the same answer and to perform a little extra work by modifying such fractions. )
He defines the complex conjugate.
Simplify (4 - 3i)/ (2 + 4i).
Solve x^2 - 3x + 10 = 0. He applies the quadratic formula and obtains the complex roots.
2) Exponential Functions (about 21 minutes)
The exponential function is f(x) = a^x. He says the notation "f(x) =" just means "y=".
He explains general form of the graph of f(x) = a^1 for the case a > 1 and the case 0 < a < 1.
He defines a^0 = 1 for "any number 'a'".
He does a "qualitative" graph for each of the following functions:
f(x) = 3^(-x).
f(x) = -2^x. (He should have mentioned that (-2)^x denotes a different function.)
f(x) = 2^(3-x).
f(x) = (2^3)(2^(-x)).
f(x) = e^ x. He introduces the number 'e'. "e is just a very special number."
3) Logarithmic Functions ( about 30 minutes)
"The opposite of an exponential is a logarithm". (Jason never talks about "inverse functions", he likes the term "opposite", but doesn't define it rigorously. He approaches this topic as a kind of "cancellation". If you have a^(log base a of w), the 'a' and the 'log to the base a' will "cancel", leaving you with the 'w'. )
He defines "y = log to the base a of x" to mean "a^y = x".
Find log to the base a of 100.
He lists the significant properties of logarithms without proving them.
If a= e then "log to the base e" is written as "ln"
"log" = "log base 10".
Write the equation 4^3 = 64 as an equation that uses logarithms.
Write the equation 10^(-3) = 0.001 as an equation that uses logarithms.
Write "log to the base 10 of 1000 = 3" as an exponential equation.
Solve: log to the base 3 of (x-4) = 2.
Solve : log to the base 5 of x^2 = -2.
Solve: log to the base 6 of (2x-3) = log base to the base 6 of 12 - log to the base 6 of 3.
Solve: log to the base 10 of x^2 = log to the base 10 of x. He explains why 0 is not a solution
Simplify: log to the base a of ( (x^2)(y)/ (z^3).
He graphs a logarithm function by asserting the fact that it is a reflection of the corresponding exponential graph about the line y = x, which he calls a "45 degree line".
4) Exponential and Log Equations (about 18 minutes)
Solve 10^x = 7.
Solve 3^(4 -x) = 5.
Solve 3^(x+4) = 2^(1-3x). He takes natural logs of both sides.
Solve log x = 1 - log(x-3). ( He eliminates x = -2 as a solution "There is no such thing as the log of a negative number.")
Solve log(5x + 1) = 2 + log(2x -3).
5) Angles ( about 42 minutes )
The best Jason can do to define an angle is "an angle is the measure of how much space there is between two lines". (I forgive him. It's actually very hard to define an angle rigorously. The usual approach in secondary education is to confuse a redundant system of parameterizing angles with the angles themselves. For example, 0 and 2 pi are "coterminal angles" (plural) but they are "really the same angle". Jason uses this approach and students will survive such contradictions. )
He defines "acute angles" and "obtuse angles".
He shows negative and positive angles drawn about the origin of the xy plane.
He shows the angles 180 deg. angle, 270 deg., 360 deg.
He shows angles greater than 360 deg.
He explains that a 450 deg. angle"is really the same measurement as 90 deg".
He introduces radians by declaring that 360 deg = 2 pi radians.
He shows angles of pi/2, pi, 3pi/2.
He draws special angles on an xy graph: 45 deg and multiples are drawn in red, 30 deg and multiples
are drawn in green.
He repeats the drawing, using radians.
He motivates the attention to special angles by saying their trig functions have simple values.
Find two positive angles coinciding with a 120 deg angle.
Find two positive angles and two negative angles that coincide with a 120 deg angle He introduces the terminology "coterminal angles".
Find two positive and two negative angles coterminal with a -30 deg angle.
Find two positive and one negative angle coterminal to an angle of (5 pi)/6.
Convert 150 degrees to radians. He explains the cancellation of units when using a conversion factor.
Convert -60 degrees to radians.
Convert 225 degrees to radians.
Convert (2 pi)/3 radians to degrees.
Convert (11 pi)/6 radians to degrees.
Disk 2
6) Finding Trig Functions Using Triangles (about 27 minutes)
He defines sine, cosine as tangent as ratios of sides in a right triangle.
He defines cotangent, secant and cosecant as reciprocals of the previous three functions.
He hints about the relation of sine,cosine and tangent to coordinates in the xy-plane.
Find all the trigonometric functions of the angle theta that is adjacent to a side of length 3 in a "3,4,5 " right triangle.
He mentions that tan(theta) = sin(theta)/cos(theta).
Find all the trigonometric function of the angle theta that is opposite to a side of length 2 in a right triangle whose hypotenuse has length 5.
7) Finding Trig Functions Using The Unit Circle (about 53 minutes)
He writes a table that shows the values of the sine,cosine and tangent of "special angles", pi/6, pi/4, pi/3. He says to memorize the table. (Jason doesn't derive these values. The usual way to do that would be to analyze an equilateral triangle with an altitude drawn in it and a square with a diagonal drawn in it.) He draws the unit circle in Cartesian coordinates.
He explains that the sine and cosine of an angle are coordinates of a point on the unit circle.
Find sin( (5 pi)/6 ).
Find cos( (5 pi)/6).
Find sin ( (2 pi)/3).
Find sin ( (4pi)/3).
Find cos ( (5pi)/6).
Find cos ( (7pi)/6).
Find sin(0).
Find sin ( pi/2).
Find cos (pi/2).
Find sin ( (3pi)/2).
Find cos ( (3pi)/2).
Find sin (pi).
Find cos(pi).
Find sin( -pi).
Find cos(-pi).
Find tan( (-5 pi)/4).
Find tan ( (-3 pi)/4).
He explains the notation "sin^-1".
Find inverse sin(1/2) ).
Find inverse sin ( (square root of 3)/2).
Find inverse cos( (- square root of 2)/2).
8) Graphing Trig Functions (about 51 minutes)
He explains how to see how the sine and cosine of an angles change as the angle changes by visualizing this on a unit circle.
Graph y = sin(theta).
He defines the amplitude and period of the wave.
Graph y = cos(theta).
Graph y = 2 sin(theta).
Graph y = sin(2 theta). (He writes the problem as "y = sin(2x)".)
Graph y = sec(theta).
Graph y = csc(theta).
Graph y = tan(theta).
9) Trig Identities (about 39 minutes)
He writes the trigonometric identities cot = 1/tan, sec = 1/cos, csc = 1/sin.
He writes the identity sin^2(theta) + cos^2(theta) = 1.
He explains the notation "sin^2".
He explains the identity using the unit circle and the Pythagorean theorm.
He writes the identity 1 + tan^2(theta) = sec^2(theta).
He writes the identity 1 + cot^2(theta) = csc^2(theta).
Verify the identity: cos(theta) sec(theta) = 1.
Verify the identity: sin(theta) sec(theta) = tan(theta).
Verify the identity: (1 + cos(theta))(1 - cos(theta)) = sin^2(theta).
Verify the identity: sin(theta)/csc(theta) + cos(theta)/sec(theta) = 1.
Verify the identity: sec(theta) - cos(theta) = tan(theta) sin(theta).
Verify the identity (sec^2(theta) - 1)/ sec^2(theta) = sin^2(theta).
Verify the identity sec^2(theta) csc^(theta) = sec^2(theta) + csc^2(theta).
Verify the identity (cot(theta) -1)/(1 - tan(theta)) = cot(theta).
Verify the identity: (sin(theta) + cos(theta))/(tan^2(theta) -1) = cos^2(theta)/ (sin(theta) - cos(theta)).
(Jason uses the careless approach to verifying identities that is traditional in secondary education. For example, in one problem he multiplies both sides of "the equation" by cos(theta) without worrying about whether cos(theta) might be zero. Coach Glonther wouldn't count this wrong.)
The video and sound are very clear, the picture is stable, and you just listen and watch while a teacher who knows his stuff and knows how to explain it takes you though the subject matter. You can pause, rewind, and watch parts over as many times as you want. You can pause and try stuff on your own with pencil and paper, or search the web or your own books for other explanations to complement what he's saying. That's one of the great things about self-paced learning.
Highly recommended.