# 5.1 Phy1020: brief trigonometry tutorial  (Page 16/20)

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A lot of data points

Once again, every other line of text in Figure 15 contains new sine and cosine values for angles that you don't have plotted yet.

Plotting all of these point is going to require a lot of pushpins and a lot of effort. Before you do that, let's think about it.

Two full cycles

You should have been able to discern by now that your plots for the sine and cosine graphs each contain two full cycles. An important thing aboutperiodic functions is that once you know the shape of the curve for any one cycle, you know the shape of the curve for every cycle from minus infinity to infinity. Theshape of every cycle is exactly the same as the shape of every other cycle.

Saving pushpins and effort

If you are running out of pushpins or running out of patience, you might consider updating your plots for only one cycle.

You should be able to discern that your curves no longer have a saw tooth shape. Each time we have run the script, we have sampledthe amplitude values of each curve at twice as many points as before. Therefore, the curves should be taking on a smoother rounded shape that is betterrepresentation of the actual shape of the curves.

Continue the process

You can continue this process of improving the curves for as long as you have the graph board space, pushpins, and patience to do so. Just divide the value of the variable named angInc by a factor of two and rerun the script. That will produce twice as many data points that are only half as far apart on thehorizontal axis.

If you choose to do so, you can plot only the new points in one-half of a cycle to get an idea of the shape. By now you should have discerned that each half of a cycle has the same shape, only onehalf is above the horizontal axis and the other half is a mirror image below the axis.

Plot of cosine and sine curves

Getting back to tactile graphics, for the benefit of any sighted person that may be assisting you, Figure 16 shows a cosine curve plotted above a sine curve very similar to the curves that you have plotted on your graph board.( Figure 16 shows a mirror image of the actual curves because the file named Phy1020a1.svg is intended to be used for manual embossing from the back of thepaper.) A non-mirror-image version is shown in Figure 20 .

Figure 16 . Mirror image plot of cosine and sine curves from the file named Phy1020a1svg.

This image contains lines that aren't straight, but with a little care, your assistant should be able to do a reasonably good job of embossing them whenthe image is printed as the full 8.5x11 inch version.

Page setup

If you use the IVEO Viewer to print the file named Phy1020a1.svg, you should use the default Page Setup selection for Letter (Landscape).

Grid lines

The image in Figure 16 contains 7 vertical grid lines. The vertical grid line in the center represents an angle of zero degrees. The space between each gridline on either side of the center represents an angle of 90 degrees or PI/2 radians.

There are two horizontal grid lines. One is one-fourth of the way down from the top. The other is one-fourth of the way up from the bottom.

how can chip be made from sand
are nano particles real
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
no can't
Lohitha
where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
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
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
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
ya I also want to know the raman spectra
Bhagvanji
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
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
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
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
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
how did you get the value of 2000N.What calculations are needed to arrive at it
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