Write the equation of a sine function that has the given characteristics.
-Amplitude: 3
Period: $4 \pi$
Phase Shift: $\frac { \pi } { 4 }$
A) $y = 3 \sin \left( \frac { 1 } { 2 } x - \frac { 1 } { 8 } \pi \right)$
B) $y = 3 \sin \left( \frac { 1 } { 2 } x + \frac { 1 } { 8 } \pi \right)$
C) $y = 3 \sin \left( 2 x + \frac { 1 } { 8 } \pi \right)$
D) $y = 3 \sin \left( 4 x + \frac { \pi } { 4 } \right)$

Question

Quizplus · Accepted Answer

The period of a sine function is given by $2\pi / b$ where $b$ is the coefficient of $x$ in the argument of the sine function. For a period of $4\pi$, $b = 1/2$, making the correct coefficient of $x$ in the argument $1/2$. The phase shift is given by $-c/b$, where $c$ is the constant added to $x$ in the argument. For a phase shift of $\pi/4$, $c/b = \pi/4$, so $c = \pi/8$. Therefore, the correct equation is $y = 3 \sin \left( \frac { 1 } { 2 } x - \frac { 1 } { 8 } \pi \right)$, which matches option A.

Write the Equation of a Sine Function That Has the Given