Unit T. BIG Question #4

• What is this video about?   In this video I explicitly focus on why sine and cosine do NOT have asymptotes and why the other four trig graphs do.  I also go over the basics of the trig functions when referencing the Unit Circle.

• What does the viewer need to pay special attention to in order to understand the concept? Although I don't quite center the attention on the visuals of the graphs, they are a big part on why I made this video. Asymptotes are what are drawn on the graphs and I simply made this video as a rationale to demonstrate the purpose of why not all of the trig graphs have them (redundant, I know! But that is how important this is if I am emphasizing it twice!!!)

Unit T. BIG Question #3

• What is this video about?   This video  goes over why a "normal" tangent graph is uphill where as a "normal" cotangent graph proceeds downhill. Besides their differences, I also detail some of the similarities between tangent and cotangent. 

• What does the viewer need to pay special attention to in order to understand the concept? Pay attention to the use of the unit circle ratios of sin(x)/cos(x) for tangent and cos(x)/sin(x) for cotangent. By understanding this, you will see why we have asymptotes where we do. Also understand how asymptotes play into the why "normal" tangent graphs are uphill and "normal" cotangent graphs are downhill.

Unit T. BIG Question #2

• What is this video about?    In this video I give an in-depth clarification on the relationship between sine and cosine parent graphs with tangent, cotangent, secant, and cosecant. I also highlight asymptotes and their role in the parent graphs of these trig function. 

• What does the viewer need to pay special attention to in order to understand the concept? For best results, be sure to pause and rewind as needed throughout the video. Don't be afraid to give your brain time to process all of the information I am throwing at you!!! 

Unit T. BIG Question #1

Unit T: BIG Question Part 1a.

 

• What is this video about? 

    This video gives a thorough explanation for the reason that sine and cosine have a period of 2pi, whereas tangent has a period of simply pi. With this information and knowledge, one will be able to understand why the graphs (whether they are parent graphs or shifted graphs) of sine, cosine, and tangent look as they do.

• What does the viewer need to pay special attention to in order to understand the concept?

     Pay attention to the importance of the Unit Circle and how that relates to why the pattern of the periods are the way they are. 

Unit T: BIG Question Part 1b.

• What is this video about? 

    This video goes over how sine and cosine have amplitudes of 1 and why the other trig function do not have amplitudes. I do cover asymptotes as well so that is basic review from previous units. The Unit Circle will be very prominent as far as amplitudes and asymptotes go.

• What does the viewer need to pay special attention to in order to understand the concept?

      When I say "You'd think their graphs would look the same..." I am comparing the cotangent parent graph to the tangent parent graph. [7:38 of the video]. Moreover, when describing cotangent I say "amplitudes" but I really meant to say "asymptotes."  Lastly, please do pay special attention to how the Unit Circle relates to the parent graphs of each trig function - I did show it many times and mentioned it countless times for a reason!!!

Student Video #5: Unit S. Concept 7. #5

• What is this video about? 

    This video goes over how to solve equations with half angles. With it, we incorporate the use of the half angle formulas. Moreover, this trigonometric concept allows us to further explore the utilization of the Unit Circle.

• What does the viewer need to pay special attention to in order to understand the concept?

      You must be able to incorporate your knowledge from past units as well, not just simply Unit S. For example, in this particular problem I was able to identify that I would need to use the Pythagorean Identity for sin^2(x). For these problems as well as this unit, you need to able to focus on what you need to do in order to solve. If that means digging through your brain for formula or proofs from past units, than so be it.     

(Unit S. Concept 4.) Half Angles Formula and it's similarity with (Unit R. Concept 1) Sum Formula

Solving the Sine, Cosine, & Tangent of 75* with Half Angle Formula

• What does this picture show?

          This picture demonstrates how to solve for a half angle using the Half Angle Formula. Although this looks difficult and challenging, it really isn't--it is just plugging in and using simple algebraic skills to solve. Please understand that this is only one of the methods used to solve for the sin(75), cos(75), and tan(75); one of the other method is demonstrated in the picture below. I have done this problem step-by-step so that it is evident how to use the Half Angle Formula in relation to half angles of the Unit Circle.

• What does the views need to pay attention to in order to understand the problem?

             The quadrant in which we determine whether sine and cosine will be a positive or negative value is dependent upon the 'u/2' NOT the 'u'. The 'u' value is twice as much as the 'u/2' value. In this case twice of 75* is 150*. Although 75* is not apart of the major angle values of the Unit Circle, 150* is. The cosine and sine used in this problem come from the ordered pair for 150*. Knowing these key parts of information along with the Half Angle Formula allow us to solve for the trig function values of half angles like 75* as shown in this example.

Solving the Sine, Cosine, & Tangent of 75* with Sum Formula

• After having solved for the sin(75), cos(75), and tan(75) using these methods, how do you know that the answers are the same?

         Without even plugging anything into your calculator, you automatically know that although the answers look different between the sin(75), cos(75), and tan(75) because different methods were used, they are same. This is because the sin(75) can only be the sin(75), cos(75) can only be equal to cos(75), and tan(75) can only be the same as tan(75). This sounds very obvious, but many people assume that because the way the answers appear are different from one another that the they are different values, but they are not. Once plugged into your calculator, you will see for yourself that the approximate answers for all of them are the same. This is what the picture below shows. 

Student Video #4: Unit S. Concept 3 - #5

• What is this video about? 

     This trigonometric video lesson goes over how to solve problems by using the     power-reducing formulas.

• What does the viewer need to pay special attention to in order to understand the concept?    

      Please understand that we substitute the power-reducing formula to the entire given trig function, not just the (x). Moreover, note that for your final answer, you want the highest power to be 1.

***DISCLAIMER: These problems look a lot scarier than they are. With practice, they become super fast, easy, and even fun! :D