Question

So I don’t understand these questions. Could you please help me? I need clearly explain.

Answer 1

The commonly form of sine function used is the following:

`y=A\sin ((2\pi)/(B)(x+C))+D`

Where:

- A is the amplitute

- B is the period

- C is the phase shift

- D is the vertical shift, or vertical translation.

For the cosine, we only change the sin to cos.

a) We have a sine function with amplitute 4 and period 3π. It is implied that there is no vertical trnslation and no phase shift, so they are 0.

Thus:

A = 4

B = 3π

C = 0

D = 0

`\begin{gathered} y=4\sin ((2\pi)/(3\pi)(x+0))+0 \\ y=4\sin ((2)/(3)x) \end{gathered}`

b) We have a sine function, amplitude 3, period 2π, vertical translation -4 and phase shift π.

Thus:

A = 3

B = 2π

C = -4

D = π

`\begin{gathered} y=3\sin ((2\pi)/(2\pi)(x+\pi))-4 \\ y=3\sin (x+\pi)-4 \end{gathered}`

c) We have a cosine function, amplitude 5, period π, vertical translation 1 and phase shift -π/2.

Thus:

A = 5

B = π

C = 1

D = -π/2

`\begin{gathered} y=5\cos ((2\pi)/(\pi)(x-(\pi)/(2)))+1 \\ y=5\cos (2x-\pi)+1 \end{gathered}`