# 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```

#### Questions & Answers

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
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
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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