MHB Basic trig question - finding the period of a sinusoid

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The discussion revolves around finding a formal representation for the period of a trigonometric function in the form f(x)=Acos(bx). A participant clarifies that the period T is determined by the angular velocity ω, expressed as T=2π/ω. The original poster acknowledges the confusion and thanks the responder for the clarification. Additionally, there is a note about formatting issues with LaTeX due to a recent operating system reinstallation. The conversation emphasizes the distinction between period and angular velocity in sinusoidal functions.
DeusAbscondus
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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;
 
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Re: basic trig question

I would say you are confusing period with angular velocity.

If given the sinusoid:

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

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

$$T=\frac{2\pi}{\omega}$$

since we may write:

$$f(t+T)=A\cos(\omega(t+T))=A\cos(\omega t+2\pi)=A\cos(\omega t)=f(t)$$
 
Re: basic trig question

MarkFL said:
I would say you are confusing period with angular velocity.

If given the sinusoid:

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

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

$$T=\frac{2\pi}{\omega}$$

since we may write:

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

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)
 
Re: basic trig question

DeusAbscondus said:
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! :)
 
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