Get reliable answers to your questions at Westonci.ca, where our knowledgeable community is always ready to help. Experience the ease of finding reliable answers to your questions from a vast community of knowledgeable experts. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.
Sagot :
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]
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]
We appreciate your time. Please come back anytime for the latest information and answers to your questions. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.