Hi crosser43,

In , b indicates the period of the sine curve.

In , 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 . So, a coefficient ofb=1 is equivalent to a period of .

To get the period of the sine curve for any coefficientb, just divide by the coefficientbto get the new period of the curve.

So, the period of is

The coefficientband the period of the sine curve have an inverse relationship, so asbgets smaller, the length of one cycle of the curve gets bigger. Likewise, as you increaseb, the period will decrease.

The zeros of the curve in the interval are .

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