Question

Write the equation of a sine function that has the following characteristics.

Amplitude: 7 Period: 9π Phase shift: 1/4

Type the appropriate values to complete the sine function.

Answer 1

`\boxed{ \displaystyle y = 7\sin\left((2)/(9)x-(1)/(4)\right)}`

Explanation:

we want to figure out the equation of a sine function that has the following characteristics.

• Amplitude: 7
• Period: 9π
• Phase shift: 1/4

the standard form of sine function is given by

`\displaystyle y = a\sin(bx-c)+d`

where:

• a is the amplitude
• b can be sorted out using the equation 2π/b=period
• C refers to phase shift

Finding a and phase shift:

a and c is simply given which is

• a=7
• C=¼

finding b:

using the equation we acquire:

`(2\pi)/(b)=9\pi`

solving the equation for b,we obtain:

b=2/9

finding d:

Since d Isn't mentioned, we would assume it 0

finding the equation:

substitute what we got:

`\boxed{ \displaystyle y = 7\sin\left((2)/(9)x-(1)/(4)\right)}`

and we're done!