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 of b=1 is equivalent to a period of .
To get the period of the sine curve for any coefficient b, just divide by the coefficient b to get the new period of the curve.
So, the period of is
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 are .
Just click on the attachments. They should clear up (I hope).