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Mama L [17]
3 years ago
8

Write an equation of the cosine function with amplitude pi/2 and period 3

Mathematics
1 answer:
juin [17]3 years ago
5 0

Answer:

y = \frac{\pi}{2}cos(\frac{2\pi}{3}x)

Step-by-step explanation:

Given

Amplitude = \frac{\pi}{2}

Period = 3

Required

Write the equivalent cosine function

The general formula is:

y = acos(bx)

Where

amplitude = |a|

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

Substitute \frac{\pi}{2} for amplitude in amplitude = |a|

|a| = \frac{\pi}{2}

a = \frac{\pi}{2}

Substitute 3 for period in period = \frac{2\pi}{b}

\frac{2\pi}{b} = 3

<em>Multiply both sides by b</em>

2\pi = 3b

<em>Divide through by 3</em>

b = \frac{2\pi}{3}

Hence;

y = acos(bx) becomes

y = \frac{\pi}{2}cos(\frac{2\pi}{3}x)

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From there, solve for x.

First get x on one side, by using the addition property of equality.

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Isolate x by adding 1.
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Lastly get x all by itself by dividing each side by 3.
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You can now substitute your x-value, 2, into one of the equations (or both, if you wish; either one will result in the same answer.)

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