What is the graph of one cycle of a sine curve with the given characteristics? Using the form y = a sin b theta, what is an equation for the sine curve

Ampltidue = 4, period 1/2pi and a

Question

What is the graph of one cycle of a sine curve with the given characteristics? Using the form y = a sin b theta, what is an equation for the sine curve

Ampltidue = 4, period 1/2pi and a < 0

anonymous · Answer

If your amplitude is four, but a is less than zero, we have to use -4 for a.  If our period is usually 2pi, and in this case it is pi/2, everything has to go four times as fast, so b is four.  That will give us a function $$f(\theta)=-4\sin (4 \theta)$$