Answer :
To find the period of the function \( y = \sin(3x) \), we use the general form of the sine function, \( y = \sin(bx) \).
In the standard function \( y = \sin(x) \), the period is \( 2\pi \). However, when the function is \( y = \sin(bx) \), the period changes based on the coefficient \( b \).
The formula for the period of \( y = \sin(bx) \) is given by:
[tex]\[ \text{Period} = \frac{2\pi}{b} \][/tex]
Here, the coefficient \( b \) is 3 (since we have \( \sin(3x) \)).
Substituting \( b = 3 \) into the formula, we get:
[tex]\[ \text{Period} = \frac{2\pi}{3} \][/tex]
So, the period of the function \( y = \sin(3x) \) is \( \frac{2\pi}{3} \).
Hence, the correct answer is:
[tex]\[ \frac{2 \pi}{3} \][/tex]
In the standard function \( y = \sin(x) \), the period is \( 2\pi \). However, when the function is \( y = \sin(bx) \), the period changes based on the coefficient \( b \).
The formula for the period of \( y = \sin(bx) \) is given by:
[tex]\[ \text{Period} = \frac{2\pi}{b} \][/tex]
Here, the coefficient \( b \) is 3 (since we have \( \sin(3x) \)).
Substituting \( b = 3 \) into the formula, we get:
[tex]\[ \text{Period} = \frac{2\pi}{3} \][/tex]
So, the period of the function \( y = \sin(3x) \) is \( \frac{2\pi}{3} \).
Hence, the correct answer is:
[tex]\[ \frac{2 \pi}{3} \][/tex]
