# 2.2 Game 2302-0320 brief trigonometry tutorial  (Page 6/17)

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The output for the opposite side

When you open your html file in your browser, the output shown in Figure 3 should appear in your browser window.

Figure 4 . Output for script in Listing 3.
```opposite = 3.999994640742543 hypotenuse = 5```

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:

5*sin(53.1301024 degrees)

The following will appear immediately below the search box:

5 * sin(53.1301024 degrees) = 4

This is the length of the opposite side for the given angle and the given length of the hypotenuse.

Interesting equations

We learned earlier that the sine of the angle is equal to the ratio of the opposite side and the hypotenuse. We also learned that the angle is thearcsine of that ratio.

If we know any two of those values ( angle , opp , hyp ), we can find the third (with a little algebraic manipulation) as shown in Figure 5 .

Figure 5 . Interesting sine equations.
```sine(angle) = opp/hyp angle = arcsine(opp/hyp)opp = hyp * sine(angle) hyp = opp/sine(angle)```

Getting back to Listing 3

After defining the radian/degree conversion functions, Listing 3 declares and initializes variables representing the length of the hypotenuse and theangle in degrees. (Note that the angle in degrees was truncated to four significant digits, which may introduce a slight inaccuracy into thecomputations.)

Get and use the sine of the angle

That angle is converted to radians and passed as a parameter to the Math.sin method, which returns the value of the sine of the angle.

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 4 . (This equation is one of the equations shown in Figure 5 .)

Looks very close to me

As you can see, the computed value for the opposite side shown in Figure 4 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 5 is used to perform the computation.) The output length for the hypotenuse is shown in Figure 4 , 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 5 .

## 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.

#### Questions & Answers

anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
Introduction about quantum dots in nanotechnology
what does nano mean?
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?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
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?
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
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
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?
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 ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
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
what is biological synthesis of nanoparticles
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
how did you get the value of 2000N.What calculations are needed to arrive at it
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