Answered

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What is the period of [tex]y = \sin(3x)[/tex]?

A. [tex]\frac{\pi}{3}[/tex]
B. [tex]\frac{2\pi}{3}[/tex]
C. [tex]3\pi[/tex]
D. [tex]6\pi[/tex]

Sagot :

GinnyAnswer
To find the period of the function \( y = \sin(3x) \), we use the general form of the sine function, \( y = \sin(bx) \).

In the standard function \( y = \sin(x) \), the period is \( 2\pi \). However, when the function is \( y = \sin(bx) \), the period changes based on the coefficient \( b \).

The formula for the period of \( y = \sin(bx) \) is given by:
[tex]\[ \text{Period} = \frac{2\pi}{b} \][/tex]

Here, the coefficient \( b \) is 3 (since we have \( \sin(3x) \)).

Substituting \( b = 3 \) into the formula, we get:
[tex]\[ \text{Period} = \frac{2\pi}{3} \][/tex]

So, the period of the function \( y = \sin(3x) \) is \( \frac{2\pi}{3} \).

Hence, the correct answer is:
[tex]\[ \frac{2 \pi}{3} \][/tex]
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