Question

Please help with number 12 -show work

Answer 1

The period of a function is the length along the x-axis that is covered by one complete cycle of the function.  Ours starts "up", so we need a period to cover up down up down (with the first "up" being our starting point).  It looks like the whole up down up down thing happens within a span of $\frac{3}{4} \pi$.The amplitude means how high does it go up the y-axis.  Ours goes up to 2 and down to negative 2, so the amplitude is 2.  For part b, the maximum values between 0 and pi/2 occur at 0 and pi/2, the minumum occur at pi/4 (there's only 1), and the zeros (where the graph goes through the x-axis) occur at pi/8 and 3pi/8.