To find the period of the function [tex]\( y = \sin(3x) \)[/tex], we need to consider the properties of the sine function and how they are affected by the coefficient of [tex]\( x \)[/tex].
The general form of the sine function is:
[tex]\[ y = \sin(bx) \][/tex]
For the sine function, [tex]\( y = \sin(bx) \)[/tex], the period [tex]\( T \)[/tex] can be calculated using the formula:
[tex]\[ T = \frac{2\pi}{b} \][/tex]
In this case, the coefficient [tex]\( b \)[/tex] is given as 3. Therefore, we substitute [tex]\( b = 3 \)[/tex] into the period formula:
[tex]\[ T = \frac{2\pi}{3} \][/tex]
After calculating, we find that:
[tex]\[ T \approx 2.0943951023931953 \][/tex]
Hence, the period of the function [tex]\( y = \sin(3x) \)[/tex] is:
[tex]\[ \frac{2\pi}{3} \][/tex]
The correct answer is:
[tex]\[ \frac{2\pi}{3} \][/tex]
