$\displaystyle y=sin2x$

1)What does the 2 indicate?

2) Is the period $\displaystyle \pi$?

3) Where are its zeroes?

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- Jul 22nd 2009, 07:48 AMcrosser43Help with answer?
$\displaystyle y=sin2x$

1)What does the 2 indicate?

2) Is the period $\displaystyle \pi$?

3) Where are its zeroes? - Jul 22nd 2009, 08:24 AMmasters
Hi crosser43,

In $\displaystyle y=\sin bx$, b indicates the period of the sine curve.

In $\displaystyle y=\sin 2x$, the period is 2.

The period of the sine curve is the length of one cycle of the curve. The natural period of the sine curve is $\displaystyle 2\pi$. So, a coefficient of**b**=1 is equivalent to a period of $\displaystyle 2\pi$.

To get the period of the sine curve for any coefficient**b**, just divide $\displaystyle 2\pi$ by the coefficient**b**to get the new period of the curve.

So, the period of $\displaystyle y=\sin 2x$ is $\displaystyle \frac{2\pi}{2}=\pi$

The coefficient**b**and the period of the sine curve have an inverse relationship, so as**b**gets smaller, the length of one cycle of the curve gets bigger. Likewise, as you increase**b**, the period will decrease.

The zeros of the curve in the interval $\displaystyle 0 \le x \le 2\pi$ are $\displaystyle \{0, \frac{\pi}{2}, \pi , \frac{3\pi}{2}, 2\pi\}$.

Just click on the attachments. They should clear up (I hope).