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The thing that looks like the hypotenuse of a right triangle is called a vector . It has a length and it has a direction. Typically, the direction is stated as the angle between the vector and the horizontal axis. Thus, thedirection is analogous to the angle at the origin in the triangle on your graph board.

Horizontal and vertical components

For reasons that I won't explain until we get to that module, you will often need to compute the horizontal and vertical components of the vector.The horizontal component is essentially the adjacent side of our current right triangle. Thus, the value of the horizontal component can be computed using thesecond equation in Figure 10 .

The vertical component is essentially the opposite side of our current right triangle, and its value can be computed using the first equation in Figure 10 .

The tangent and arctangent of an angle

Once again, although the tangent of an angle is based on very specific geometric considerations involving circles (see (External Link) ), for our purposes, the tangent of an angle is simply a ratio between the lengths of two different sides of a righttriangle.

A ratio of two sides

For our purposes, we will say that the tangent of an angle is equal to the ratio of the opposite side and the adjacent side. Therefore, in the case of the3-4-5 triangle that you have on your graph board, the tangent of the angle at the origin is equal to 4/3 or 1.333.

Not limited to 1.0

Note that the absolute value for the sine and the cosine of an angle is limited to a maximum value of 1.0. However, the tangent of an angle is not solimited. In fact, the tangent of 45 degrees is 1.0 and the tangent of 90 degrees is infinity. This results from the length of the adjacent side, which is thedenominator in the ratio, going to zero at 90 degrees.

Dividing by zero in a script is usually not a good thing. This is a pitfall that you must watch out for when working with tangents. I will provide code later on that shows you how deal with this issue.

Computing the tangent

If we know the lengths of the opposite side and the adjacent side, we can compute the tangent and use it for other purposes later without having to knowthe value of the angle.

Conversely, if we know the value of the angle but don't know the lengths of the adjacent side and/or the opposite side, we can obtain the tangent valueusing a scientific calculator or lookup table and use it for other purposes later.

The tangent of an angle -- sample computation

Enter the following into the Google search box:

tan(53.13010235415598 degrees)

The following will appear immediately below the search box:

tan(53.13010235415598 degrees) = 1.33333333

This agrees with the ratio that we computed earlier .

The arctangent (inverse tangent) of an angle

The arctangent of an angle is the value of the angle having a given tangent value. (For example, as mentioned above, the arctangent of infinity is 90degrees and the arctangent of 1.0 is 45 degrees.) In other words, if you know the value of the tangent of an unknown angle, you can use a scientific calculator or lookup table to find the value of theangle.

Questions & Answers

anyone know any internet site where one can find nanotechnology papers?
Damian Reply
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
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
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.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
many many of nanotubes
what is the k.e before it land
what is the function of carbon nanotubes?
I'm interested in nanotube
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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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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