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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

how can chip be made from sand
Eke Reply
are nano particles real
Missy Reply
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
Lale Reply
no can't
Lohitha
where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
has a lot of application modern world
Kamaluddeen
yes
narayan
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
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
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
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
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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