Write the equation of a sine function that has the given characteristics.
-Amplitude: 3
Period: $5 \pi$
Phase Shift: $- \frac { \pi } { 5 }$
A) $y = 3 \sin \left( \frac { 2 } { 5 } x + \frac { 2 } { 25 } \pi \right)$
B) $y = 3 \sin \left( \frac { 2 } { 5 } x - \frac { 2 } { 25 } \pi \right)$
C) $y = 3 \sin \left( \frac { 5 } { 2 } x - \frac { 2 } { 25 } \pi \right)$
D) $y = 3 \sin \left( 6 x - \frac { \pi } { 6 } \right)$

Question

Quizplus · Accepted Answer

The equation of a sine function is given by $y = A \sin(Bx + C)$, where A is the amplitude, B is the frequency, and C is the phase shift. In this case, the amplitude is 3, the period is $5 \pi$, and the phase shift is $- \frac { \pi } { 5 }$. The frequency is given by $B = \frac { 2 \pi } { \text{period} }$, so in this case, $B = \frac { 2 \pi } { 5 \pi } = \frac { 2 } { 5 }$. Substituting these values into the equation, we get $y = 3 \sin \left( \frac { 2 } { 5 } x - \frac { \pi } { 5 } \right)$.

Write the Equation of a Sine Function That Has the Given