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

Answer 1

I shall use x instead of whatever character you chose to copy/paste.

The graph of y = a sin bx has
amplitude = |a|
period = 2π/b

so, what do you get?

Answer 2

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

Answer 3

The graph of one cycle of the sine curve with the given characteristics would look like:

Graph of sine curve with given characteristics

To write an equation for this sine curve using the form y = a sin bθ:

Since amplitude = 4, a = -4 (because a < 0)

Since period = 1/4π, we can find b using the formula:

period = 2π/b

1/4π = 2π/b

b = 8

Therefore, the equation of the sine curve is:

y = -4 sin 8θ