The Trigonometry and Pre-Calculus Tutor - 2 DVD Set! - 5 Hour Course!
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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!
Section 1: Complex Numbers
Section 2: Exponential Functions
Section 3: Logarithmic Functions
Section 4: Solving Exponential and Logarithmic Equations
Section 5: Angles
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
Top customer reviews
I want to say a couple things about the videos overall, and then about this specific one. The videos are meant to be a supplement to a textbook and class. In none of the DVDs I have purchased so far has Jason covered every topic that was discussed in class. He focuses on the foundation topics from which others build. If you think you can just study the material on the DVDs then show up for quiz and test days and get an A in the class, you are greatly mistaken. The best you could hope for with that plan is probably a C. If you know the core/fundamental material well, which this will give you, you will be well prepared to tackle the more difficult concepts that will be presented in class.
As for this DVD in particular, it focuses almost exclusively on the trigonometry, and less so on the algebra. The way most college level pre-calculus classes are set up, including the one I am in, is you do a review of algebra then get into the trig. The only algebra presented in this DVD are exponential and logarithmic functions and complex numbers. I am sure that Jason did not want to be too duplicative with the material on his algebra DVDs, which is probably why he focused more on the trigonometry. I know one of the reviews for this DVD said something along the lines of "this does not cover all the material in a pre-calc class." That is most likely the reason why.
As I said in a review of one of the algebra DVDs, this is a no frills presentation. It is a guy in front of a white board doing multiple problems. It is not exciting or flashy. Whether you are going to find this useful depends on your learning style. If you can learn just watching a lecture style presentation, but one in which you cannot interact and ask questions of the instructor, these will be very useful. If you are someone who learns more by asking questions and interacting and find the idea of watching someone do math problems on TV mind numbing, then you are not going to find this useful and would probably benefit more from a tutor.
Now that I have finished my class I wanted to provide an update to this review. As I said in the comment to one of the other reviews for this product, and somewhat above, there was no perfect way for Jason to make this DVD. That has about as much to do with how many pre-calculus classes are structured as it is anything else. If you use this along with his advanced algebra tutor set, you will get about 90% of all the material covered in most college level pre-calc classes. You really have to look at those as one long DVD set. Most of what is in the trig/pre-calc DVD will not be covered in college algebra, but a lot of what is covered in the advanced algebra DVD will be at least touched on in pre-calc. That is not even to say everything in the trig/pre-calc DVD will be covered in every pre-calc class either. In my class for example we did not spend any time on imaginary/complex numbers.
As for what is included in the trigonometry portion, Jason does go through all the fundamental concepts you need to learn to do well. It is the stuff that if you do not understand it, you will be hopelessly lost when you get to the more advanced material. The one change I would have made to the DVD is I would have included more of the trig identities like the double angle and half angle identities, and included a section on conics. That said, the information he does give about manipulating the trig identities are the most used, and the most important ones to memorize. Finally, you have to keep in mind this is a five hour DVD set. There is no way to distill 10-15 weeks worth of information into five hours. It is imperative to look at this as a supplemental tool, not a replacement for going to class and doing homework. Anyone who looks at this as a replacement for those things will fail miserably and have no one to blame but themselves.
Jason has released a second part to this set that fills in many of the gaps in what he did not cover here. The Trigonometry & Pre-Calculus Tutor - Volume 2 - 6 Hour Course! It covers more of the trig identities like the half angle and double angle, even-odd, etc. There is also a section on covering trig equations and a lot of material on the law of sines and cosines. As I originally said in my review it covers the things that should have been in the original release with the exponential, logarithm and imaginary number stuff taken out. Personally I think those subjects would have been better served to be on one of his algebra DVDs. It had to be a judgment call though, and due to the fact that there is not a lot of uniformity between how and when trig is presented in a school's curriculum there was no perfect way to do it. If you go to a school where trig is presented as a single class than this set will be better, especially when added with volume 2. If however your school does a review of algebra then goes into trig then this will seem very lacking. But, given that Jason had already put out two advanced algebra DVDs, it was not practical to put all that material on this one as well. Nor should he have to apologize for referring people back to the other set if they need to brush up on algebra concepts. In all, if you have this set, volume 2 of this set, and his algebra DVDs, the only thing you will be missing is the material on conics that you will hit at some point. Those are really about using algebra to study circles, ellipses, parabolas and hyperbolas. They are not something you will use trig for, so if your algebra skills are good you will be OK. Some pre calc classes also start introducing you to the concepts of vectors (to get you ready for physics), but Jason does cover those extensively in his physics tutor DVD set The Ultimate Physics Tutor - 11 Hour Course! - 2 DVD Set! - Learn By Examples!.
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.
( I use the customary notation "x^p" to mean "x raised to the p power".)
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 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.
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 ( pi/2).
Find cos (pi/2).
Find sin ( (3pi)/2).
Find cos ( (3pi)/2).
Find sin (pi).
Find sin( -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.
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