$\displaystyle y=sin2x$
1)What does the 2 indicate?
2) Is the period $\displaystyle \pi$?
3) Where are its zeroes?
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).