Write the equation of a sine function that has the given characteristics.
-Amplitude: 5
Period: 3
A) $y = 4 \sin ( 3 x )$
B) $y = 5 \sin \left( \frac { 2 } { 3 } \pi x \right)$
C) $y = 3 \sin \left( \frac { 1 } { 2 } \pi x \right)$
D) $y = \sin ( 3 \pi x ) + 4$

Question

Quizplus · Accepted Answer

The general form of a sine function is $y = A \sin(Bx)$, where $A$ is the amplitude and the period $P$ is given by $P = \frac{2\pi}{B}$. For an amplitude of 5 and a period of 3, we solve for $B$ using the period formula: $3 = \frac{2\pi}{B}$, which gives $B = \frac{2\pi}{3}$. Thus, the correct equation is $y = 5 \sin \left( \frac { 2 } { 3 } \pi x \right)$.

Write the Equation of a Sine Function That Has the Given