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Figure 12 . Output for script in Listing 7.
opposite = 3.9999851132269173 adjacent = 3

Very similar code

The code in Listing 7 is very similar to the code in Listing 3 and Listing 5 . The essential differences are that

  • Listing 3 uses the sine along with the opposite side and the hypotenuse.
  • Listing 5 uses the cosine along with the adjacent side and the hypotenuse.
  • Listing 7 uses the tangent along with the opposite side and the adjacent side.

You should be able to work through those differences without further explanation from me.

The cotangent of an angle

There is also something called the cotangent of an angle, which is simply the ratio of the adjacent side to the opposite side. If you know how to work withthe tangent, you don't ordinarily need to use the cotangent, so I won't discuss it further.

Computing length of opposite side with the Google calculator

We could also compute the length of the opposite side using the Google calculator.

The length of the opposite side -- sample computation

Enter the following into the Google search box:

3*tan(53.1301024 degrees)

The following will appear immediately below the search box:

3 * tan(53.1301024 degrees) = 4.00000001

Dealing with different quadrants

Up to this point, we have dealt exclusively with angles in the range of 0to 90 degrees (the first quadrant). As long as you stay in the first quadrant, things are relatively straightforward.

As you are probably aware, however, angles can range anywhere from 0 to 360 degrees (or more). Once you begin working with angles that are greater then 90 degrees,things become a little less straightforward.

Another svg file

When you downloaded the zip file named Phy1020.zip using the link given above , you should also have found that the zip file contains a file named Phy1020a1.svg.

The purpose of this file is to make it possible for you to create tactile graphics for sine and cosine curves using the procedure explained in the earliermodule named Manual Creation of Tactile Graphics .

If you have the ability to create tactile graphics, you don't need to perform the work in the following graph board exercise. However, you shouldread about it anyway because that will probably help you to better understand the sine and the cosine of an angle.

I will get back to tactile graphics after I describe the graph board exercise.

Another graph board exercise

In this graph board exercise, we will plot a graph of the amplitude of the sine of an angle on the vertical axis versus the angle itself onthe horizontal.

We will also do the same thing for the cosine. It would be very good if you could plot one curve on the top half of your graph board and the other curve onthe bottom half of your graph board so that you can easily compare the two.

Interpreting gridline values

Since I don't know how many tactile grid lines there are on your graph board, I can't tell you exactly how to interpret the grid lines so as to make maximumuse of the space on the board. All that I can tell you is that the vertical amplitude values for each curve will range from -1.0 to +1.0. We would like toplot values from -360 degrees to + 360 degrees on the horizontal. You should interpret the values of the gridlines on your graph board accordingly.

Questions & Answers

what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
How can I make nanorobot?
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
how can I make nanorobot?
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
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Source:  OpenStax, Contemporary math applications. OpenStax CNX. Dec 15, 2014 Download for free at http://legacy.cnx.org/content/col11559/1.6
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