Answer:
π
Step-by-step explanation:
The period of a sine function is the horizontal length it takes for the function to complete one full cycle. For the function [tex] y = 3 \sin(2x) [/tex], the period is determined by the coefficient in front of [tex] x [/tex] inside the sine function.
The general form of a sine function is [tex] y = \sin(bx) [/tex], where [tex] b [/tex] affects the period.
The period [tex] T [/tex] of the function [tex] y = \sin(bx) [/tex] is given by:
[tex] T = \dfrac{2\pi}{|b|} [/tex]
For the function [tex] y = 3 \sin(2x) [/tex], [tex] b = 2 [/tex].
Therefore, the period [tex] T [/tex] is:
[tex] T = \dfrac{2\pi}{|2|} \\\\ = \dfrac{\pi}{1} \\\\= \pi [/tex]
So, the period of the function [tex] y = 3 \sin(2x) [/tex] is [tex] \pi [/tex] radians.
