Question

If a sine curve has a vertical shift down 19 units with an amplitude of 21, what will the minimum and maximum values be? (i.e. how high and low will the graph go?)
Min Value:
Max Value:

Answer 1

Given:

Amplitude = 21

Vertical shift = 19 units down

To find:

The maximum and the minimum value.

Solution:

The general form of sine function is:

$y=A\sin (Bx+C)+D$

Where, |A| is amplitude, $\dfrac{2\pi}{B}$ is period, $-\dfrac{C}{B}$ is phase shift and D is the vertical shift.

Here,

$Maximum=D+A$

$Minimum=D-A$

We have,

Amplitude: $A = 21$

Vertical shift: $D=-19$

Negative sign means shifts downwards.

Now,

$Maximum=D+A$

$Maximum=-19+21$

$Maximum=2$

And,

$Minimum=D-A$

$Minimum=-19-21$

$Minimum=-40$

Therefore, the minimum value is -40 and the maximum value is 2.