Question

A sinusoid with amplitude 6 has a minimum value of 4. What is its maximum value?

Answer 1

Answer: Max Value is y = 16

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Explanation:

The amplitude is the vertical distance from the horizontal center line to either the peak or valley.

The minimum value is 4. The distance from the min value to the center is 6 units. So the center is at 4+6 = 10.

Then we go another 6 units up to arrive at the max value 10+6 = 16

Refer to the diagram below. I recommend drawing out a sine curve along with  the vertical y axis number line.

Answer 2

Answer:

The maximum value: 16

Step-by-step explanation:

Given

• Amplitude A = 6

• Minimum value min = 4

We know that a function's amplitude A can be interpreted as the difference between the average between its maximum and minimum and its minimum.

$A\:=\:\frac{max+min}{2}-min$

solving for max

$2A\:=\:max+min\:-2\:min$

$2A+2\:min=max+min$

$\:2\left(A+min\right)=max+min$

$max\:=2\left(A+min\right)-min$

substituting A = 6 and min = 4

$max\:=2\left(6+4\right)-4$

$max=\:2\left(10\right)-4$

$max\:=\:20-4$

$max = 16$

Therefore, the maximum value: 16