Question

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

Answer 1

GIVEN:

Amplitude:– 7

Period:– 9π

Phase shift:– 1/4

ANSWER:

As we know that,

y = A sin{B(x + C)} + D, where A is amplitude; B is the period; C is the phase shift & D is the vertical shift.

Since, we know period is 2pi/B, Phase shift is -C & vertical shift is D.

So, y = 7sin{2π/9(x - 1/4)} + 0

y = 7sin{π(2/9x - 1/18}.

Answer 2

Answer:

$\displaystyle y = 7\sin(9\pi(x + {1}/{4}) )$

Step-by-step explanation:

we are given

• Amplitude:7
• Period:9π
• Phrase shift:¼

remember that,

$\displaystyle y = A \sin(B(x + C) )+ D$

where A is the Amplitude

B is the Period

C is the Phase shift

D is the vertical shift

note that, since D isn't given we'll take it 0

altogether substitute:

$\displaystyle y = 7\sin(9\pi(x + {}^{1}/_{4}) )+ 0$

hence,

our equation is

$\displaystyle y = 7\sin(9\pi(x + {}^{1}/_{4}) )$

and we are done!