Question

question 2 of 10
what is the equation of the sinusoid?

a. ( y=sin (pi x) )
b. ( y=sin (2 x) )
c. ( y=sin left(\frac{1}{2} x
ight) )
d. ( y=sin x )

Explanation:

Step1: Identify period of the sinusoid

From the graph, the period \( T = \pi \) (distance between two consecutive zeros, e.g., 0 to \( \pi \)).

Step2: Calculate angular frequency \( \omega \)

Use \( \omega = \frac{2\pi}{T} \). Substitute \( T = \pi \):
\( \omega = \frac{2\pi}{\pi} = 2 \)

Step3: Determine the equation

The sinusoid passes through (0,0) with amplitude 1, so equation is \( y = \sin(2x) \).

Answer:

B. \( y = \sin(2x) \)