A sine function has the following key features: Period = π Amplitude = 2 Midline: y=−2 y-intercept: (0,-2) The function is a reflection of its parent function over the x-axis. Use the sine tool to graph the function. The first point must be on the midline and the second point must be a maximum or minimum value on the graph closest to the first point.

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kudzordzifrancis kudzordzifrancis · Answer 1 · 2020-02-16T12:35:50+01:00

Answer:

Use the points as shown in the attachment to obtain the graph shown.

Step-by-step explanation:

Based on the description, the sine function is of the form.

[tex]y = - a \: \sin \: bx + c[/tex]

We use the formula for the period to find the b value.

[tex] \frac{2 \pi}{b} = \pi[/tex]

This implies that:

[tex] \frac{2}{b} = 1 \\ \implies \: b = 2[/tex]

The a-value is the amplitude, which is 2

The negative sign shows a reflection over the x-axis.

Since the mid line is y=-2, the value of c is -2 because the parent function moved down from 2 units.

This means the mid-line moved from 0 to -2

Therefore the equation is

[tex]y = - 2 \sin 2x - 2[/tex]

ibiscollingwood ibiscollingwood · Answer 2 · 2022-02-11T03:21:37+01:00

The function of sine will be, [tex]y=-2sin(2x )-2[/tex]

It is given as, [tex]y=Asin(wx)+c[/tex]

Where A is amplitude , w is angular frequency.

Given that, A = 2 , frequency [tex]f=\frac{1}{\pi}[/tex] and mid line, c= -2

Angular frequency, [tex]w=2\pi f=2\pi *\frac{1}{\pi} =2[/tex]

Substitute all values in standard equation of sine.

We get, [tex]y=2sin(2x )-2[/tex]

Since, The function is a reflection of its parent function over the x-axis.

Thus, Standard equation of sine function will be,

[tex]y=-2sin(2x )-2[/tex]

The graph of function attached below.

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