160k views
5 votes
What is the period of y=sin(3x)

2 Answers

6 votes

Answer:

B: 2pi/3

Explanation:

What is the period of y=sin(3x)-example-1
User Coolbeet
by
9.6k points
5 votes
The new period is 2/3 π.

The period of the two elementary trig functions, sin(x) and cos(x) is .
If we multiply the input variable by a constant has the effect of stretching or contracting the period. If the constant, c>1 then the period is stretched, if c<1 then the period is contracted.We can see what change has been made to the period, T, by solving the equation:
cT=2πWhat we are doing here is checking what new number, T, will effectively input the old period, 2π, to the function in light of the constant. So for our givens:3T=2π
T=2/3 πOther method to solve this;sin3x=sin(3x+2π)=sin[3(x+2π/3)]=sin3xThis means "after the arc rotating three time of (x+(2π/3)), sin 3x comes back to its initial value"
So, the period of sin 3x is 2π/3 or 2/3 π.
User Daniel Rosenthal
by
7.7k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories