# TrigonometryBasic trig question - finding the period of a sinusoid

#### DeusAbscondus

##### Active member
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)$$where A is amplitude and b is period Thanks, D'abs​ Attached Thumbnails PS: sorry about sloppy maths: been away for months and seem to have forgotten use of$$ to wrap around text to create latex;

#### MarkFL

Staff member
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

##### Active member
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.

Hope this helps!