Question

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Answer 1

Answer:

There you go:

$y = 4 \cos(4\pi \: t + \frac{\pi}{4} )$

$y = a\cos(w\: t + \alpha )$

$w = 4\pi$

$2\pi \: f = 4\pi$

$f = 2$

Answer 2

Answer:

$\displaystyle 2$

Step-by-step explanation:

$\displaystyle y = Acos(Bx - C) + D$

When working with a trigonometric equation like this, always remember the information below:

$\displaystyle Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A|$

So, the first procedure is to find the period of this graph, and when calculated, you should arrive at this:

$\displaystyle \boxed{\frac{1}{2}} = \frac{2}{4\pi}\pi$

You will then plug this into the frequency formula, $\displaystyle T^{-1} = F.$ Look below:

$\displaystyle \frac{1}{2}^{-1} = F \\ \\ \boxed{2 = F}$

Therefore, the frequency of motion is two hertz.

I am delighted to assist you at any time.