Question

what is the graph of one cycle of a sine curve with the given characteristics? Using the form y = a sin B, what is an equation for the sine curve amplitude = 3, period = 2 pi , and a > 0

Answer 1

so amplitude means how high the graph goes. usually is y = sin(b), it means that the highest value is 1 (sin (pi/2)) and the lowest value is -1 (sin(3.pi/2)). to get a high value of 3, you would need to multiply the highest value of the sine curve by 3 (1 x 3 = 3). so,
3 = a x sin(pi/2)
then, 3=a x (1). thus, a = 3.

the next part of the question is a little trickier. the period is how long it takes for the sine curve to get back to its original position. this means that if it start at 0 (sin(0 radians)), at which "b" value will y = 0 again. this period is changed by dividing and multiplying the value of "b" inside the sin function. example = sin(b/2), sin(2b)
normally, with no changed, sin(b) has a period of 2pi. thus you dont need to change anything inside the sine function to get a period of 2pi.

so, taking all that together, we have a = 3 and the inside of the sine function is just normally b.

so, y=3 x sine(b), having an amplitude of 3 and a period of 2pi.

Answer 2

Would it be this

Answer 3

Or this one? @GuardianOfLore

Answer 4

the first one. :) one cycle of a sine curve means it must return to the same point with wthe same degree value (2pi radians = 0 radians). that was my mistake. but yes you got the basic point.

Answer 5

Thanks so much :)