Question

What is the period of the function \( y=\sin 9 x ? \) Select one:

A). \( \frac{\π}{9}\)
B) . \( \frac{-2 \π}{9} \)
C). \( \frac{2 \π}{9}\)
D). \( \frac{9}{2 \π\)

Answer 1

The period of the function
`\(y = \sin 9x\) is \( (2\π)/(9) \)` determined by dividing
`\(2\π\)` by the coefficient of
`\(x\)` which is 9.

So.the correct option is C.

Step-by-step explanation:

The period of a trigonometric function is the length of one complete cycle of the function. For the function
`\(y = \sin 9x\)` the coefficient of
`\(x\)` is 9. The general formula for the period of a sine or cosine function is
`\( (2\π)/(n) \)` where
`\(n\)` is the coefficient of
`\(x\)`. In this case the period
`\(T\)` is given by
`\(T = (2\π)/(9)\)`.

When
`\(x\)` varies from
`\(0\)` to
`\(T\)` the sine function completes one full oscillation. In other words it takes
`\( (2\π)/(9) \)` units of
`\(x\)` for
`\(y\)` to repeat its values. The larger the coefficient of
`\(x\)` the shorter the period indicating a faster oscillation.

Understanding the period is crucial in graphing and analyzing trigonometric functions as it helps identify key features such as amplitude and frequency.In summary, for
`\(y = \sin 9x\)` the period is
`\( (2\π)/(9) \)` signifying that the function completes one cycle over this interval of
`\(x\)`.

So.the correct option is C.