# 5.1 Phy1020: brief trigonometry tutorial  (Page 12/20)

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For example, we know that the tangent of the angle at the origin on your graph board is 1.333. From that, we can determine the value of the angle.

The arctangent of an angle -- sample computation

Enter the following into the Google search box:

arctan(4/3) in degrees

The following will appear immediately below the search box:

arctan(4/3) = 53.1301024 degrees

We can also write a JavaScript script to perform the calculation.

Getting the angle for a known tangent value using JavaScript

Please create an html file containing the code shown in Listing 6 and open it in your browser.

Listing 6 . Arctan of 3-4-5 triangle.
```<!-- File JavaScript06.html --><html><body><script language="JavaScript1.3">function toRadians(degrees){ return degrees*Math.PI/180}//end function toRadians //============================================//function toDegrees(radians){ return radians*180/Math.PI}//end function toDegrees //============================================//var opp = 4 var adj = 3var ratio = opp/adj var angRad = Math.atan(ratio)var angDeg = toDegrees(angRad) document.write("radians = " + angRad + "</br>") document.write("degrees = " + angDeg)</script></body></html>```

The output from the script

Once again, when you open this file in your browser, the output shown in Figure 5 should appear in your browser window.

The code in Listing 6 is very similar to the code in Listing 2 . They both describe the same right triangle, so the output should be thesame in both cases.

The code in Listing 2 uses the opposite side and the hypotenuse along with the arcsine to compute the angle. The code in Listing 6 uses the opposite side and the adjacent side along with the arctangent to compute the angle. Otherwise,no further explanation should be required.

Interesting tangent equations

In the spirit of Figure 7 and Figure 8 , Figure 11 provides some interesting equations that deal with the angle, the opposite side, and the adjacent side.Given any two, you can find the third using either the tangent or arctangent.

Figure 11 . Interesting tangent equations.
```tangent(angle) = opp/adj angle = arctangent(opp/adj)opp = tangent(angle) * adj adj = opp/tangent(angle)```

An exercise involving the tangent

Please copy the code from Listing 7 into an html file and open it in your browser.

Listing 7 . Finding the length of the opposite side.
```<!-- File JavaScript07.html --><html><body><script language="JavaScript1.3">function toRadians(degrees){ return degrees*Math.PI/180}//end function toRadians //============================================//function toDegrees(radians){ return radians*180/Math.PI}//end function toDegrees //============================================//var adj = 3 var angDeg = 53.13var angRad = toRadians(angDeg) var tangent = Math.tan(angRad)var opp = adj * tangent document.write("opposite = " + opp + "</br>") adj = opp/tangentdocument.write("adjacent = " + adj + "</br>")</script></body></html>```

When you open your html file in your browser, the output shown in Figure 12 should appear in your browser window. We can see that the values in Figure 12 are correct for our 3-4-5 triangle.

find the 15th term of the geometric sequince whose first is 18 and last term of 387
I know this work
salma
The given of f(x=x-2. then what is the value of this f(3) 5f(x+1)
hmm well what is the answer
Abhi
how do they get the third part x = (32)5/4
can someone help me with some logarithmic and exponential equations.
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
I don't understand what the A with approx sign and the boxed x mean
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
oops. ignore that.
so you not have an equal sign anywhere in the original equation?
hmm
Abhi
is it a question of log
Abhi
🤔.
Abhi
I rally confuse this number And equations too I need exactly help
salma
But this is not salma it's Faiza live in lousvile Ky I garbage this so I am going collage with JCTC that the of the collage thank you my friends
salma
Commplementary angles
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
hii
Uday
hi
salma
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
a perfect square v²+2v+_
kkk nice
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
rolling four fair dice and getting an even number an all four dice
Kristine 2*2*2=8
Differences Between Laspeyres and Paasche Indices
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
how do you translate this in Algebraic Expressions
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
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.
what is nano technology
what is system testing?
preparation of nanomaterial
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
what is system testing
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
how did you get the value of 2000N.What calculations are needed to arrive at it
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