Using Sine and Cosine functions in real life?

[Goldenboko]

In Pre-Calculus I have an assignment, "To Illistrate how a sine or cosine function is applied in the real world."

Honestly, I haven't the slightest clue. Help?

EDIT: Can't radio waves be graphed as sine/cosine functions?

[Tavrobel]

Let's say you've got a bullet lodged into a wall. It's in there at a certain angle. Now imagine that this bullet came from a sniper's rifle. By measuring the height of surrounding buildings, the elevation of the bullet on the wall, and distances to and from possible roof levels of other buildings, you can use Trigonometry to figure out where the sniper was.

Or you can rotate a sine function with bounds from limit "a" to limit "b," rotate it around an axis, and get a volume for a sine-shaped random volume.

Sin and Cos are also used heavily in Physics formulas in order to generate numbers necessary to do... stuff.

Or you can say cosine looks like a flower pot.

[Goldenboko]

Apparently the teacher wants the actual graphs he mentions how the period and amplitude change things. I researched radio waves, and this site gives me all the info I need. (http://www.thetartan.org/2007/9/17/scitech/work) Assuming the frequency of the graph is the same thing as the period.

[Tavrobel]

The frequency is not the period. It's its reciprocal. As in, how often it occurs in a given set, whereas period gives you the time needed to repeat itself.

Example, sin has a period of 2pi. Its frequency would be 1/(2pi). Amplitude stretches the graph up and down; it is usually the coefficient outside of the function. In the equation a*sin(bx) + c, a is your amplitude value, b affects the period, and c shifts it along the y axis.

[blackmage_nuke]

Techno Music.
A sine wave is a common sound used. The frequency of the middle A note is 440hz and amplitude controls the volume.

It can also be used to represent the swing of a pendulum with the amplitude being the maximum distance from the normal and the frequency being the actual frequency of the swing. I think it can be used to show the velocity too but i forget how.

[Goldenboko]

The frequency is not the period. It's its reciprocal. As in, how often it occurs in a given set, whereas period gives you the time needed to repeat itself.

Example, sin has a period of 2pi. Its frequency would be 1/(2pi). Amplitude stretches the graph up and down; it is usually the coefficient outside of the function. In the equation a*sin(bx) + c, a is your amplitude value, b affects the period, and c shifts it along the y axis.

Ah I see. Would the period of a radio wave always be the same since no modulation notes a change in the period, only in the frequency? :confused:

[Tavrobel]

It can also be used to represent the swing of a pendulum with the amplitude being the maximum distance from the normal and the frequency being the actual frequency of the swing. I think it can be used to show the velocity too but i forget how.

Take a derivative. It's something like -4cos(4pi) with a bunch of coefficients everywhere, based on a particular pendulum.


Ah I see. Would the period of a radio wave always be the same since no modulation notes a change in the period, only in the frequency? :confused:

If you change the period, the frequency must also be changed. If one is given as b, and one is given as 1/b, there can't be any way for you to change b and not have those values both be different from their previous iteration.

[blackmage_nuke]

When you have an AM radio, the frequncy and period are constant and the amplitude stretches and contracts to represent the information in the signal.
When you have an FM radio the frequncy stretches and contracts while the amplitude stays the same.

Though strictly speaking a sine wave will only carry a blank signal, when you start putting actual data into the radio wave then its not really a sine wave anymore.

[Goldenboko]

So then FM would be manipulating either the period, speed of the wave, or both?

[blackmage_nuke]

You cant manipulate the speed of the wave, radio waves travel at the speed of light, but yes it manipulates the period.

[Goldenboko]

You cant manipulate the speed of the wave, radio waves travel at the speed of light, but yes it manipulates the period.

Oh yeah! Duh! *remembers failing through chemistry*
EDIT: Thanks guys, I think I can write this paper, and do this poster now~

[rubah]

power outlets. the AC electricity frequency is 60 hz, which is the crest of a sine wave going through the point 60 times in a second. (or the trough, or whatever point you'd like)

[Aerith's Knight]

Electromagnetics, Optics, Surface calculations, Quantum physics, you name it.

Pick one and I'll give you three examples.

[Goldenboko]

Already did the project. Good try though! =D

[blackmage_nuke]

Wait a minute, you get assignments, in maths?

Thats ridiculus!