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 amplitude of a sine function is given by the coefficient of the sine term, which is 5 in option B. The period of a sine function is given by $ \frac{2\pi}{b} $, where $b$ is the coefficient of $x$ inside the sine function. For a period of 3, we solve $ \frac{2\pi}{b} = 3 $ to find $ b = \frac{2\pi}{3} $, which matches the coefficient of $x$ in option B.

Write the Equation of a Sine Function That Has the Given