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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). \( \frac{9}{2 \π\)

1 Answer

7 votes

Final Answer:

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.

User Redhwan
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