Question

Help please!! asap no wrong answers will give the crown symbol

Answer 1

Answer:

$\displaystyle 4$

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:

$\displaystyle \boxed{\frac{1}{4}} = \frac{2}{8\pi}\pi$

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

$\displaystyle \frac{1}{4}^{-1} = F \\ \\ \boxed{4 = F}$

Therefore, the frequency of motion is four hertz.

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Answer 2

Answer:

4Hz

Step-by-step explanation:

Standard form of a sine or cosine function,

y = acos(b(x+c))

where a is the amplitude, b is the value to find the period. and c is the phase shift.

Period = \frac{2\pi}{b}

From the equation given in the question,

$y = 3cos(8\pi \: t + \frac{\pi}{2} ) \\ y = 3cos(8\pi(t + \frac{1}{16} )) \: \: (factorising \: 8\pi \: out)$

We can see:

Amplitude = 3,

Period = \frac{2\pi}{8\pi} = 1 / 4

Phase Shift = 1 / 16

Now we want to find the frequency.

Frequency = 1 / Period

= 1 / (1/4)

= 4Hz