Answer:
Second option: [tex]\frac{2\pi }{3}[/tex]
Step-by-step explanation:
In Trigonometry there are six functions. These functions are:
1) Sine (sin).
2) Cosine (cos).
3) Tangent (tan).
4) Secant (sec).
5) Cosecant (csc).
6) Cotangent (cot).
For this exercise it is important to know that, given a Sine function in the following form:
[tex]ASin(Bx)[/tex]
"A" is the Amplitude and the Period of the function is:
[tex]\frac{2\pi }{|B|}[/tex]
In this case you have the following Sine function given in the exercise:
[tex]y = sin(3x)[/tex]
So, you can identify that:
[tex]A=1\\\\B=3[/tex]
Therefore, in order to find the Period of the funtion given, you need to substitute the value of "B" into [tex]\frac{2\pi }{|B|}[/tex].
Then, you get:
[tex]\frac{2\pi }{|3|}=\frac{2\pi }{3}[/tex]
As you can notice, the Period obtained matches with the one given in the Second option.
