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The value for the sine of the angle is then used in an algebraic equation to compute the length of the opposite side, which is displayed in Figure 6 . (This equation is one of the equations shown in Figure 7 .)

Looks very close to me

As you can see, the computed value for the opposite side shown in Figure 6 is extremely close to the known value of 4 units.

Re-compute the length of the hypotenuse

After that, the value of the hypotenuse is re-computed (as though it were the unknown in the problem) using the value of the sine and the recently computedvalue of the opposite side. (Once again, one of the equations from Figure 7 is used to perform the computation.) The output length for the hypotenuse is shown in Figure 6 , and it matches the known value.

Example usage of Math.asin and Math.sin methods

Listing 2 and Listing 3 provide examples of how to use the JavaScript Math.asin and Math.sin methods to find the angle, the opposite side, or the hypotenuse of a right triangle when the other two areknown as shown by the equations in Figure 7 .

The cosine and arccosine of an angle

You are going to find the discussion in this section to be very similar to the discussion in the previous section on the sine and the arcsine of an angle.

Once again, although the cosine of an angle is based on very specific geometric considerations involving circles (see (External Link) ), for our purposes, the cosine 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 cosine of an angle is equal to the ratio of the adjacent side and the hypotenuse. Therefore, in the case of the3-4-5 triangle that you have on your graph board, the cosine of the angle at the origin is equal to 3/5 or 0.6.

As before, if we know the lengths of the hypotenuse and the adjacent side, we can compute the cosine and use it to determine the value of the angle. (We willdo this later.)

Conversely, if we know the value of the angle but don't know the lengths of the hypotenuse and/or the adjacent side, we can obtain the cosine value (theratio of the adjacent side and the hypotenuse) using a scientific calculator or lookup table and use it for other purposes later.

The cosine of an angle -- sample computation

Enter the following into the Google search box:

cos(53.13010235415598 degrees)

The following will appear immediately below the search box:

cos(53.13010235415598 degrees) = 0.6

This matches the ratio of the adjacent side to the hypotenuse for a 3-4-5 triangle.

The arccosine (inverse cosine) of an angle

The arccosine of an angle is the value of the angle having a given cosine value. In other words, if you know the value of the cosine of an unknown angle,you can use a scientific calculator or lookup table to find the value of the angle.

Getting the angle for a known cosine value

For example, we know that the cosine of the angle at the origin on your graph board is 0.6. From that, we can determine the value of the angle using eitherthe Google calculator or JavaScript.

Questions & Answers

what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
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
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
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.
Bharti
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
Daniel
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
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
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
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
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.
Tarell
what is the actual application of fullerenes nowadays?
Damian
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.
Tarell
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.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
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.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
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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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