What is the period of y = sin(3x)? StartFraction pi Over 3 EndFraction StartFraction 2 pi Over 3 EndFraction 3 pi 6 pi

Question

asked Apr 12, 2021 60.8k views

2 Answers

FalconC · Answer 1 · 2021-04-16T09:22:34+0000

Answer:

Second option:
$(2\pi )/(3)$

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:

ASin(Bx)

"A" is the Amplitude and the Period of the function is:

$(2\pi )/(|B|)$

In this case you have the following Sine function given in the exercise:

y = sin(3x)

So, you can identify that:

$A=1\\\\B=3$

Therefore, in order to find the Period of the funtion given, you need to substitute the value of "B" into
$(2\pi )/(|B|)$ .

Then, you get:

$(2\pi )/(|3|)=(2\pi )/(3)$

As you can notice, the Period obtained matches with the one given in the Second option.