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 = 3, period = 2, and a > 0 (1 point) Responses The graph starts at the point left-parenthesis 0 comma 0 right-parenthesis. The function then increases up to the point left-parenthesis start fraction pi over 4 end fraction comma 3 right-parenthesis. It then decreases, passing through the point left-parenthesis start fraction pi over 2 end fraction comma 0 right-parenthesis, down to the point left-parenthesis start fraction 3 pi over 4 end fraction comma negative 3 right-parenthesis. It then increases up the point left-parenthesis pi comma 0 right-parenthesis and ends. y = 3 sin 2Θ Image with alt text: A portion of a graph of a sine function is shown. The graph starts at the point left-parenthesis 0 comma 0 right-parenthesis. The function then increases up to the point left-parenthesis start fraction pi over 4 end fraction comma 3 right-parenthesis. It then decreases, passing through the point left-parenthesis start fraction pi over 2 end fraction comma 0 right-parenthesis, down to the point left-parenthesis start fraction 3 pi over 4 end fraction comma negative 3 right-parenthesis. It then increases up the point left-parenthesis pi comma 0 right-parenthesis and ends. y = 3 sin 2 Θ The graph starts at the point left-parenthesis 0 comma 0 right-parenthesis. The function then decreases down to the point left-parenthesis start fraction pi over 4 end fraction comma negative 3 right-parenthesis. It then increases, passing through the point left-parenthesis start fraction pi over 2 end fraction comma 0 right-parenthesis, up to the point left-parenthesis start fraction 3 pi over 4 end fraction comma 3 right-parenthesis. It then decreases down the point left-parenthesis pi comma 0 right-parenthesis and ends. y = 3 sin 2Θ Image with alt text: A portion of a graph of a sine function is shown. The graph starts at the point left-parenthesis 0 comma 0 right-parenthesis. The function then decreases down to the point left-parenthesis start fraction pi over 4 end fraction comma negative 3 right-parenthesis. It then increases, passing through the point left-parenthesis start fraction pi over 2 end fraction comma 0 right-parenthesis, up to the point left-parenthesis start fraction 3 pi over 4 end fraction comma 3 right-parenthesis. It then decreases down the point left-parenthesis pi comma 0 right-parenthesis and ends. y = 3 sin 2 Θ The graph starts at the point left-parenthesis 0 comma 0 right-parenthesis. The function then increases up to the point left-parenthesis start fraction pi over 2 end fraction comma 3 right-parenthesis. It then decreases, passing through the point left-parenthesis pi comma 0 right-parenthesis, down to the point left-parenthesis start fraction 3 pi over 2 end fraction comma negative 3 right-parenthesis. It then increases up the point left-parenthesis 2 pi comma 0 right-parenthesis and ends. y = 3 sin Θ Image with alt text: A portion of a graph of a sine function is shown. The graph starts at the point left-parenthesis 0 comma 0 right-parenthesis. The function then increases up to the point left-parenthesis start fraction pi over 2 end fraction comma 3 right-parenthesis. It then decreases, passing through the point left-parenthesis pi comma 0 right-parenthesis, down to the point left-parenthesis start fraction 3 pi over 2 end fraction comma negative 3 right-parenthesis. It then increases up the point left-parenthesis 2 pi comma 0 right-parenthesis and ends. y = 3 sin Θ The graph starts at the point left-parenthesis 0 comma 0 right-parenthesis. The function then increases up to the point left-parenthesis pi comma 3 right-parenthesis. It then decreases down to the point left-parenthesis 2 pi comma 0 right-parenthesis and ends. y= 3 sin Θ
The correct response is: The graph starts at the point (0,0). The function then increases up to the point (π/4, 3). It then decreases, passing through the point (π/2, 0), down to the point (3π/4, -3). It then increases up to the point (π, 0) and ends. y = 3 sin 2Θ
