# 5.1 Phy1020: brief trigonometry tutorial  (Page 15/20)

 Page 15 / 20

Not really a saw tooth

The sine and cosine curves don't really have a saw tooth shape. That is an artifact of the fact that we didn't compute enough points to reliablydescribe the shape of the curves. Let's improve on that.

Modify the script

Modify the code in your script to initialize the value of the variable named angInc to 45 degrees instead of 90 degrees and then load the revised version into your browser. This will cause thescript to fill in data points between the points that we already have producing the output shown in Figure 16 .

Figure 14 . Sinusoidal values at 45-degree increments.
```Angle: -360 Sine: 0 Cosine: 1 Angle: -315 Sine: 0.71 Cosine: 0.71Angle: -270 Sine: 1 Cosine: 0 Angle: -225 Sine: 0.71 Cosine: -0.71Angle: -180 Sine: 0 Cosine: -1 Angle: -135 Sine: -0.71 Cosine: -0.71Angle: -90 Sine: -1 Cosine: 0 Angle: -45 Sine: -0.71 Cosine: 0.71Angle: 0 Sine: 0 Cosine: 1 Angle: 45 Sine: 0.71 Cosine: 0.71Angle: 90 Sine: 1 Cosine: 0 Angle: 135 Sine: 0.71 Cosine: -0.71Angle: 180 Sine: 0 Cosine: -1 Angle: 225 Sine: -0.71 Cosine: -0.71Angle: 270 Sine: -1 Cosine: 0 Angle: 315 Sine: -0.71 Cosine: 0.71Angle: 360 Sine: 0 Cosine: 1```

Plot the new points

Every other line of text in Figure 14 should contain sine and cosine values for angles that are half way between the points that you already have plotted.Use pushpins to plot the new points and connect all of the points in each curve using rubber bands, pipe cleaners, or whatever you find most useful forthis purpose.

Same shape but shifted horizontally

The two curves still have the same shape, although shifted horizontally relative to one another and they are still periodic. However, they no longerhave a saw tooth shape. They tend to be a little more rounded near the peaks and they are beginning to provide a better representation of the actual shapes ofthe sine and cosine curves.

Let's do it again

Change the value of the variable named angInc from 45 degrees to22.5 degrees and load the new version of the html file into your browser. Now the output should look like Figure 15 .

Figure 15 . Sinusoidal values at 22.5-degree increments.
```Angle: -360 Sine: 0 Cosine: 1 Angle: -337.5 Sine: 0.38 Cosine: 0.92Angle: -315 Sine: 0.71 Cosine: 0.71 Angle: -292.5 Sine: 0.92 Cosine: 0.38Angle: -270 Sine: 1 Cosine: 0 Angle: -247.5 Sine: 0.92 Cosine: -0.38Angle: -225 Sine: 0.71 Cosine: -0.71 Angle: -202.5 Sine: 0.38 Cosine: -0.92Angle: -180 Sine: 0 Cosine: -1 Angle: -157.5 Sine: -0.38 Cosine: -0.92Angle: -135 Sine: -0.71 Cosine: -0.71 Angle: -112.5 Sine: -0.92 Cosine: -0.38Angle: -90 Sine: -1 Cosine: 0 Angle: -67.5 Sine: -0.92 Cosine: 0.38Angle: -45 Sine: -0.71 Cosine: 0.71 Angle: -22.5 Sine: -0.38 Cosine: 0.92Angle: 0 Sine: 0 Cosine: 1 Angle: 22.5 Sine: 0.38 Cosine: 0.92Angle: 45 Sine: 0.71 Cosine: 0.71 Angle: 67.5 Sine: 0.92 Cosine: 0.38Angle: 90 Sine: 1 Cosine: 0 Angle: 112.5 Sine: 0.92 Cosine: -0.38Angle: 135 Sine: 0.71 Cosine: -0.71 Angle: 157.5 Sine: 0.38 Cosine: -0.92Angle: 180 Sine: 0 Cosine: -1 Angle: 202.5 Sine: -0.38 Cosine: -0.92Angle: 225 Sine: -0.71 Cosine: -0.71 Angle: 247.5 Sine: -0.92 Cosine: -0.38Angle: 270 Sine: -1 Cosine: 0 Angle: 292.5 Sine: -0.92 Cosine: 0.38Angle: 315 Sine: -0.71 Cosine: 0.71 Angle: 337.5 Sine: -0.38 Cosine: 0.92Angle: 360 Sine: 0 Cosine: 1```

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
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.
what is nano technology
what is system testing?
how did you get the value of 2000N.What calculations are needed to arrive at it
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