Unit T Big Question Blog Post #4

4) Why do sine and cosine not have asymptotes, but the other four trig graphs do? Use unit circle ratios to explain.

Sin and cos don’t have asymptotes but other trig functions do because cos is x/r which is x/1 on the unit circle. If r was 0 then it would be undefined but in this case r can't be 0, it is always 1. This is the same thing for sin which is y/r or y/1 and why they don’t have asymptotes. Sec and csc in the other hand do have asymptotes because sec is 1/cos and whenever cosine is 0 then it is undefined which makes it an asymptote. Csc is 1/sin and whenever sin is 0 the answer would also have an asymptote. For tan it equals sin/cos and whenever cos is 0 then the answer would be undefined which will have an asymptote. Cot it is cos/sin and whenever sin is 0 it will also be an asymptote. This is why sin and cos aren’t asymptotes but the other trig functions are.

https://wiki.eee.uci.edu/images/6/6e/Triangle_on_unit_circle.jpg

Unit T Big Question Blog Post #3

3) Why is a normal tangent graph uphill, but a normal cotangent graph downhill? Use the unit circle ratios to explain.


Normal tangent graph is uphill because tan is sin/cos and when cosine equals 0 it is undefined which is in 90 degrees (pi/2) and 270 degrees (3pi/2). Those are asymptotes and when we graph and label asymptotes and follow the Unit circle, tan is shown positive because the arrow goes up to the asymptote. Cot is cos/sin, when sine is 0 it is 0 degrees, pi, and 2pi which are asymptotes and when labeled, the positive is at the asymptote towards zero and once drawn we see that it is downhill.

cot

tan

http://www.cartage.org.lb/en/themes/Sciences/Mathematics/Trigonometry/differentfund/different%20Functions%20.html

http://jwilson.coe.uga.edu/emat6680fa06/crumley/unit/6_files/image010.jpg

Unit T Big Question #2

How do the graphs of sine and cosine relate to each of the others? Emphasize asymptotes in your response. 

     a.Tangent? When cosine is zero, it makes tangent become undefined. It will have an asymptote on the points where cos = 0: pi/2 or 3pi/2.  

     b. Cotangent? 

    

Cot is the inverse of tan because tan is sin/cos. Cot is cos/sin. When sin is 0, there is an asymptote because the whole thing is made undefined at that particular part. Tan asymptotes are at pi/2 and 3pi/2 so, to contrast, this means that cot asymptotes are at 0 and pi. Using the graphs, the asymptotes of the graph y = tanx are the x intercepts of the graph of y = cotx. There are vertical asymptotes at each end of the cycle. The asymptote that occurs at pi repeats every pi units.

      

c. secant?

sec is the inverse of cos which means that it is 1/cos and when cosine is 0 in this case, sec becomes undefined as a whole since it is the reciprocal of cosine. When we have undefined as our answer there is going to be an asymptote. These are vertical asymptotes.  The asymptote that occurs at pi/2 repeats every  pi units. The brown lines are the sec graph. The pink line is part of the parent graph of cos.

d. cosecant?

csc is the reciprocal of sin making csc 1/sin. So, when sin is zero in this case, cos becomes undefined anytime sin is 0, thus resulting in an asymptote. The x intercepts of y = sin x are the asymptotes for y = csc x. There are vertical asymptotes. The asymptote that occurs at pi repeats every pi units  

the red is the csc graph and the blue is the parent graph of sin. 

  

    http://www.regentsprep.org/Regents/math/algtrig/ATT7/othergraphs.html

   

Unit T Big Question #1

How do the trig graphs relate to the unit Circle?

    a. Period?- Why is the period for sine and cosine 2pi, whereas the period for tangent and cotangent is pi?

b. Amplitude?- How does the fact that sine and cosine have amplitudes of one relate to what we know about the Unit Circle?


a. sine and cosine has a period of 2pi because it takes 360 degrees (2pi) for the period to repeat again. Whereas it only takes tangent and cotangent 180 degrees (pi) for the period to repeat.

b. cosine and sine only have amplitudes of 1 because it has no asymptotes and in the unit circle they both can equal 1 depending which radians. Tangent can only equal 0 or be undefined.  For csc and sec they are the reciprocals of sin and cosine and when it divided by 0 then it is undefined.

Student Video 7: Unit S Concept 7

This video is about how to solve a problem from Unit S concept 7 using a variety of skills learned from the past and to this unit. This problem will solve number 5 in concept 7.

The reader should pay attention to the steps and listen to how certain identities seem to appear out of know where. The reader should have some Unit circle jnowlege and skills from the last two units.

Unit S. Concept 4 Student problem

Solving Sine, Cosine, and Tangent of 100 with Half Angle Formula

This picture show how to solve a unit S concept 4 level problem using half angle formulas.

Students must remember that determining if sin or cos is + or - depends strictly on u/2 not u, they should know that these problems need basic unit circle skills to solve these problems.

Solving sin cos tan with Sum Formulas

This picture shows that you can solve for the same answers using the sum formula, you can also use the difference formula and get the same answer.

The student should know how to use the sum and difference formula. They should also pay attention to the work done in this student problem.

In conclusion we know that the answers are the same because when plugged into the calculator they get the same answers.

Unit S. Concept 3 PQ #5

This video is about how to solve a specific problem using power reducing formulas.

The viewer needs to understand how I used the power reducing formula to solve the specific problem. Note that even though the variables may be similar does not mean they can simplify. The power should be 1 that is the point of power reducing.