Basic trig question - finding the period of a sinusoid

[DeusAbscondus]

Would someone kindly take a look at my geogebra snapshot attached,
and tell me a more formal way of representing the formula for the period of a trig function of form:

f(x)=Acos(bx)$$
where A is amplitude and b is period

Thanks,
D'abs​

http://www.mathhelpboards.com/images/mhb/misc/paperclip.png Attached Thumbnailshttp://www.mathhelpboards.com/attachment.php?attachmentid=753&d=1366260749


PS: sorry about sloppy maths: been away for months and seem to have forgotten use of $$ to wrap around text to create latex;

 

[MarkFL]

Re: basic trig question

I would say you are confusing period with angular velocity.

If given the sinusoid:

\(\displaystyle f(t)=A\cos(\omega t)\)

then the angular velocity is $\omega$ and the period $T$ is:

\(\displaystyle T=\frac{2\pi}{\omega}\)

since we may write:

\(\displaystyle f(t+T)=A\cos(\omega(t+T))=A\cos(\omega t+2\pi)=A\cos(\omega t)=f(t)\)

 

[DeusAbscondus]

Re: basic trig question

I would say you are confusing period with angular velocity.

If given the sinusoid:

\(\displaystyle f(t)=A\cos(\omega t)\)

then the angular velocity is $\omega$ and the period $T$ is:

\(\displaystyle T=\frac{2\pi}{\omega}\)

since we may write:

\(\displaystyle f(t+T)=A\cos(\omega(t+T))=A\cos(\omega t+2\pi)=A\cos(\omega t)=f(t)\)

Thanks kindly Mark.
This clears up my query.
(I also just realized why my $$s aren't working: i have re-installed OS and have yet to re-install a Tex program)

 

[Jameson]

Re: basic trig question

Thanks kindly Mark.
This clears up my query.
(I also just realized why my \$\$s aren't working: i have re-installed OS and have yet to re-install a Tex program)

If you're referring to your original post then I believe you just forgot the opening pair of dollar signs. You wrote: f(x)=Acos(bx)\$\$ but you need to write \$\$f(x)=Acos(bx)\$\$ and it will output:

$$f(x)=Acos(bx)$$

Hope this helps! :)

 

[CellCoree]

I'll go and re-read the rulesSure, I'd be happy to help with your question about finding the period of a sinusoid. The period of a trigonometric function is the length of one complete cycle of the function. In the case of a cosine function, the period is the distance from one peak to the next peak, or from one trough to the next trough.

To find the period of a trigonometric function of the form f(x)=Acos(bx), we can use the formula:

Period = 2π/b

So, in your case, the period would be:

Period = 2π/b

Where b is the coefficient in front of x in the function f(x)=Acos(bx).

In terms of representing this formula more formally, we could write it as:

f(x)=Acos(bx) ⇒ Period = 2π/b

This shows that the period is equal to 2π divided by the coefficient b.

I hope this helps and clarifies the formula for finding the period of a trigonometric function. Let me know if you have any other questions.