# 5.1 Phy1020: brief trigonometry tutorial  (Page 18/20)

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We often think of a two-dimensional space with horizontal and vertical axes and the origin at the center in quadrants. Each quadrant is bounded byhalf the horizontal axis and half the vertical axis.

If you measure the angle between the positive horizontal axis and a line segment thatemanates from the origin, quadrant 1 contains angles between 0 and PI/2, quadrant 2 contains the angles between PI/2 and PI, quadrant 3 contains theangles between PI and 3*PI/2, and quadrant 4 contains the angles between 3*PI/2 and 2*PI (or zero). (Note that I didn't attempt to reconcile the inclusion ofeach axis in the two quadrants on either side of the axis.)

It is sometimes useful to consider how the algebraic sign of the sine, cosine, and tangent values varies among the four quadrants. Figure 17 contains a table that shows the sign of the sine, cosine, and tangent values for each ofthe four quadrants

Figure 17 . Algebraic signs versus quadrants.
```1 2 3 4 sine + + - -cosine + - - + tangent + - + -```

Working with arctangents is more difficult than arcsine or arccosine

Working with arctangent is somewhat more difficult than working with arcsine or arccosine, if for no other reason than the possibility of dividing by zerowhen working with the arctangent.

Listing 9 shows a JavaScript function named getAngle that deals with this issue.

Listing 9 . A function to deal with quadrants.
```<!---------------- File JavaScript09.html ---------------------><html><body><script language="JavaScript1.3">document.write("Start Script</br>"); //The purpose of this function is to receive the adjacent// and opposite side values for a right triangle and to // return the angle in degrees in the correct quadrant.function getAngle(adjacent,opposite){ if((adjacent == 0)&&(opposite == 0)){ //Angle is indeterminate. Just return zero.return 0; }else if((adjacent == 0)&&(opposite>0)){ //Avoid divide by zero denominator.return 90; }else if((adjacent == 0)&&(opposite<0)){ //Avoid divide by zero denominator.return -90; }else if((adjacent<0)&&(opposite>= 0)){ //Correct to second quadrantreturn Math.atan(opposite/adjacent)*180/Math.PI + 180; }else if((adjacent<0)&&(opposite<= 0)){ //Correct to third quadrantreturn Math.atan(opposite/adjacent)*180/Math.PI + 180; }else{//First and fourth quadrants. No correction required. return Math.atan(opposite/adjacent)*180/Math.PI;}//end else }//end function getAngle//Modify these values and run for different cases. var adj = 3;var opp = 4; document.write("adj = " + adj.toFixed(2) +" opp = " + opp.toFixed(2) + " units</br>"); document.write("angle = " + getAngle(adj,opp).toFixed(2)+ " units</br>"); var adj = -3;var opp = 4; document.write("adj = " + adj.toFixed(2) +" opp = " + opp.toFixed(2) + " units</br>"); document.write("angle = " + getAngle(adj,opp).toFixed(2)+ " units</br>"); var adj = -3;var opp = -4; document.write("adj = " + adj.toFixed(2) +" opp = " + opp.toFixed(2) + " units</br>"); document.write("angle = " + getAngle(adj,opp).toFixed(2)+ " units</br>");var adj = 3; var opp = -4;document.write("adj = " + adj.toFixed(2) + " opp = " + opp.toFixed(2) + " units</br>"); document.write("angle = " + getAngle(adj,opp).toFixed(2)+ " units</br>");</script></body></html>```

what is variations in raman spectra for nanomaterials
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
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
what is the stm
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?
what is a peer
What is meant by 'nano scale'?
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
what is Nano technology ?
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?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
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?
research.net
kanaga
sciencedirect big data base
Ernesto
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 did you get the value of 2000N.What calculations are needed to arrive at it
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