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State the amplitude and period of f(x) = 3cos9/5t

User Jeanm
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1 Answer

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Answer:

The amplitude is 3 and the period is 10π/9.

Explanation:

The standard cosine function is in the form:


y=a\cos(b(x-c))+d

Where |a| is the amplitude, 2π/b is the period, c is the phase shift, and d is the vertical shift.

We have the function:


f(x)=\displaystyle 3\cos(9)/(5)t

We can rewrite this as:


\displaystyle f(x)=(3)\cos\left((9)/(5)\left(t-0\right)\right)-(0)

Therefore, a = 3, b = 9/5, c = 0, and d = 0.

Hence, our amplitude is |3| = 3.

Our period will be:


\displaystyle \text{Period}=(2\pi)/(9/5)=2\pi \cdot (5)/(9)=(10\pi)/(9)

User Radamanthus
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