Question

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Answer 1

The equation of the sinusoidal function is y = -2sin(x + 1.5) - 3

The sinusoidal function

The minimum and the maximum of the function are

• Minimum = -1
• Maximum = -5

The amplitude (A) is calculated as:

A = 0.5 * (Maximum - Minimum)

So, we have:

A = 0.5 * (-5 + 1)

A = -2

The vertical shift (d) is calculated as:

d = 0.5 * (Maximum + Minimum)

So, we have:

d = 0.5 * (-5 - 1)

d = -3

The period (P) is calculated as:

P = 2π/B

From the graph,

B = 1

So, we have:

P = 2π/1

P = 2π

So, the amplitude is -2 and the period is 2π.

The equation of the sine function

In (a), we have:

A = -2

B = 1

d = -3

A sine function is represented as:

y = A sin(Bx + C) + D

So, we have:

y = -2sin(x + C) - 3

The graph passes through the point (0, -5)

So, we have

-5 = -2sin(0 + C) - 3

Solve for C, we have

C = 1.5

So, we have:

y = -2sin(x + 1.5) - 3

Hence, the equation of the sinusoidal function is y = -2sin(x + 1.5) - 3

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