# 5.1 Phy1020: brief trigonometry tutorial  (Page 17/20)

 Page 17 / 20

The curves

A cosine curve is plotted with vertical values relative to the top grid line. It extends from -360 degrees on the left to +360 degrees on the right.

A sine curve is plotted with vertical values relative to the bottom grid line. It also extends from -360 degrees on the left to +360 degrees on theright. (Note once again that Figure 16 was flipped horizontally to crate a mirror image.)

Return values for the Math.asin, Math.acos, and Math.atan methods

I told you earlier that the Math.asin method returns a value between -PI/2 and PI/2. However, I didn't tell you that the Math.acos method returns a value between 0 and PI, or that the Math.atan method returns a value between -PI/2 and PI/2. You now have enough informationto understand why this is true.

Smooth curves

If you examine the two curves that you have just plotted, you can surmise that the sine and cosine functions are smooth curves whose values range between-1 and +1 inclusive. For every possible value between -1 and +1, there is an angle in the range -PI/2 and PI/2 whose sine value matches that value. There isalso an angle in the range 0 and PI whose cosine value matches that value.

(Although you haven't plotted the curve for the tangent, a similar situation holds there also.)

An infinite number of angles

Therefore, given a specific numeric value between -1 and +1, there are an infinite number of angles whose sine and cosine values match thatnumeric value and the method has no way of distinguishing between them. Therefore, the Math.asin method returns the matching angle that is closest to zero and the Math.acos method returns the matching positive angle that is closest to zero.

What can we learn from this?

One important thing that we can learn is there is no difference between the sine or cosine of an angle and the sine or cosine of a different anglethat differs from the original angle by 360 degrees. Thus, the Math.asin and Math.acos methods cannot be used to distinguish between angles that differ by 360 degrees. (As you learned above, the situation involving the Math.asin and Math.acos methods is even more stringent than that.)

One-quarter cycle contains all of the information

Another thing that we can learn is that once you know the shape of the cosine curve from 0 degrees to 90 degrees, you have enough information to construct theentire cosine curve and the entire sine curve across any range of angles. Every possible value or the negative of every possible value that can occur in a sineor cosine curve occurs in the cosine curve between 0 degrees and 90 degrees. Furthermore, the order of those values is also well defined.

You should think about these kinds of relationships. As I mentioned earlier, as long as we are working with angles between 0 and 90 degrees, everything isrelatively straightforward. However, once we start working with angles between 90 degrees and 360 degrees (or greater), things become a little lessstraightforward.

If you have a good picture in your mind of the shape of the two curves between -360 degrees and +360 degrees, you may be able to avoid errors once you start working on physics problems that involve angles outsidethe range of 0 to 90 degrees.

find the 15th term of the geometric sequince whose first is 18 and last term of 387
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
Commplementary angles
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
hii
Uday
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
Privacy Information Security Software Version 1.1a
Good
Got questions? Join the online conversation and get instant answers!