sin(x), sin(2x), sin(1/2)....what is the period?

**stupidguy** · September 5th 2010, 11:23 PM

sin(x), sin(2x), sin(1/2)....what are the periods?

Pls explain to me the concepts involved so I can remember more clearly.

Thanks.

**Educated** · September 6th 2010, 01:47 AM

A period is how long it takes for the wave to complete one full cycle.

Sin(x) has a period of 2 $\pi$ in radians, or $360^{\circ}$ in degrees. This means that if you draw the graph of sin(x), the graph would take 2 $\pi$ or $360^{\circ}$ to complete one full cycle. Which is a period.

Sin(2x) has a period of half of sin(x)
Sin(0.5x) has a period of double of sin(x)

The 2 in front of the x doubles the speed of one wave, which means that it halves the time, and since a period is the length of time for one full cycle, the period is halved as well. Vise versa for the 0.5.

Just think of it as this way:

$sin(x) = \text{Normal period}$

$sin(2x) = \frac{\text{Normal period}}{2}$

$sin(0.5x) = \frac{\text{Normal period}}{0.5}$

**Archie Meade** · September 6th 2010, 03:43 AM

Originally Posted by stupidguy

sin(x), sin(2x), sin(1/2)....what are the periods?

Pls explain to me the concepts involved so I can remember more clearly.

Thanks.

$\displaystyle\ Sin(0)=0, \; \; Sin\left(\frac{{\pi}}{2}\right)=1, \; \; Sin({\pi})=0,\; \; Sin\left(\frac{3{\pi}}{2}\right)=-1,\; \; Sin(2{\pi})=0$

$Sinx$ goes through a full period in $2{\pi}$ radians.

Finding 3 consecutive zeros will discover the period, as the centreline of the graph is the x-axis.
Simplest is to start at zero.

$\displaystyle\ Sin(2x)=0$ for $\displaystyle\ x=0$ and $\displaystyle\ 2x={\pi}\Rightarrow\ x=\frac{{\pi}}{2}$ and $2x=2{\pi}\Rightarrow\ x={\pi}$

therefore $Sin(2x)$ has period ${\pi}$ radians.

$\displaystyle\ Sin\left(\frac{x}{2}\right)=0\Rightarrow\ x=0, \;\; x=2{\pi}, \;\; x=4{\pi}$

so the period of $\displaystyle\ Sin\left(\frac{x}{2}\right)$ is $4{\pi}$ radians.

Alternatively......

$SinA=Sin(A+2{\pi})$

$Sinx=Sin(x+2{\pi})$ has a period of $2{\pi}$ radians

$Sin(2x)=Sin(2x+2{\pi})=Sin[2(x+{\pi})]$ which therefore has a period of ${\pi}$ radians

$\displaystyle\ Sin\left(\frac{x}{2}\right)=Sin\left(\frac{x}{2}+2 {\pi}\right)=Sin\left[\frac{1}{2}(x+4{\pi})\right]$ has a period of $4{\pi}$ radians

**stupidguy** · September 6th 2010, 04:42 AM

Originally Posted by Educated

A period is how long it takes for the wave to complete one full cycle.

Sin(x) has a period of 2 $\pi$ in radians, or $360^{\circ}$ in degrees. This means that if you draw the graph of sin(x), the graph would take 2 $\pi$ or $360^{\circ}$ to complete one full cycle. Which is a period.

Sin(2x) has a period of half of sin(x)
Sin(0.5x) has a period of double of sin(x)

The 2 in front of the x doubles the speed of one wave, which means that it halves the time, and since a period is the length of time for one full cycle, the period is halved as well. Vise versa for the 0.5.

Just think of it as this way:

$sin(x) = \text{Normal period}$

$sin(2x) = \frac{\text{Normal period}}{2}$

$sin(0.5x) = \frac{\text{Normal period}}{0.5}$

You are talking in the context of physics becos u use terms like speed and wave. LOL

**yeKciM** · September 6th 2010, 07:52 AM

just to add that if you have shifted signal ( $\sin {x \pm A}$ ), left or right it will have same period but just moved to one or another side

or if you multiply signal for example that "sin" ( $A\sin {x}$ ) it will again have same period but just amplitude bigger or smaller depending by which number is multiplying (if it is more or less than 1)... same thing when looking at those signals of yours if it's variable (in this case "x") is multiplied with number bigger than 1 that means that it will change that many times faster than usual, and if is multiplied with number less than 1 it will go that many times slower than normal

Thread: sin(x), sin(2x), sin(1/2)....what is the period?

LinkBack

Thread Tools

Display

sin(x), sin(2x), sin(1/2)....what is the period?

Similar Math Help Forum Discussions

what is the period

[SOLVED] Future value annuities with a different payment period to the compounding period.

Period : 2

Period

Period

Search Tags