Welcome to Westonci.ca, where you can find answers to all your questions from a community of experienced professionals. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

Find the period and amplitude of the function.

[tex]\[ y = 4 \sin 6x \][/tex]

Give the exact values, not decimal approximations.

Period: [tex]\(\boxed{\frac{\pi}{3}}\)[/tex]

Amplitude: [tex]\(\boxed{4}\)[/tex]


Sagot :

To find the period and amplitude of the function [tex]\( y = 4 \sin 6x \)[/tex], let's follow these steps:

1. Identify the amplitude:
- The amplitude of a sine function [tex]\( y = A \sin(Bx) \)[/tex] is given by the absolute value of the coefficient of the sine function.
- In the given function [tex]\( y = 4 \sin 6x \)[/tex], the coefficient of the sine term is 4.
- Therefore, the amplitude is [tex]\( \boxed{4} \)[/tex].

2. Determine the period:
- The period of a sine function [tex]\( y = A \sin(Bx) \)[/tex] is calculated using the formula:
[tex]\[ \text{Period} = \frac{2\pi}{B} \][/tex]
- In the given function [tex]\( y = 4 \sin 6x \)[/tex], the coefficient [tex]\( B \)[/tex] in front of [tex]\( x \)[/tex] is 6.
- Substituting [tex]\( B = 6 \)[/tex] into the period formula, we get:
[tex]\[ \text{Period} = \frac{2\pi}{6} = \frac{\pi}{3} \][/tex]
- Thus, the exact value of the period is [tex]\( \boxed{\frac{\pi}{3}} \)[/tex].

So, the exact values are:
- Amplitude: [tex]\( \boxed{4} \)[/tex]
- Period: [tex]\( \boxed{\frac{\pi}{3}} \)[/tex]