Sinusoidal Modeling Quiz

The correct answer is y = 5 cos x because the equation y = 5 cos x represents a cosine function with an amplitude of 5, which means the graph will oscillate between -5 and 5. The cosine function has a period of 2π, so the graph will repeat itself every 2π units along the x-axis.

The graph of cosine begins at (0,1) because at the starting point of the graph, which is at x=0, the value of cosine is 1. As x increases or decreases from 0, the value of cosine changes accordingly, but at x=0, the value is always 1.

This graph represents the cosine (cos) trigonometric function. The cosine function is a periodic function that oscillates between -1 and 1, with a period of 2π. It is used to describe the relationship between the angles and sides of a right triangle. The graph of the cosine function starts at its maximum value of 1, decreases to its minimum value of -1, and then repeats this pattern indefinitely.

The amplitude of a graph refers to the maximum displacement or distance from the equilibrium position. In this case, the amplitude is given as 3, which means that the graph reaches a maximum displacement of 3 units from the equilibrium position.

The graph represents the cosine (cos) trigonometric function. The cosine function is a periodic function that oscillates between -1 and 1. It represents the x-coordinate of a point on the unit circle as it rotates counterclockwise. The graph of the cosine function starts at its maximum value of 1, then decreases to its minimum value of -1, and repeats this pattern indefinitely. Therefore, the correct answer is "Cos".

The given equation is in the form y = A*cos(Bx + C), where A = 4, B = 5, and C = 2π/5. The period of a cosine function is given by 2π/B. Therefore, the period of y = 4cos5x is 2π/5. Since the given equation has an additional term of 2π/5, the period is still 2π/5. Hence, the answer is True.

The equation y=2sin2x represents a sinusoidal function with an amplitude of 2 and a period of π. The coefficient of 2 in front of sin(2x) stretches the graph vertically by a factor of 2. Therefore, the given graph is indeed represented by the equation y=2sin2x.

This graph represents the cosine (cos) trigonometric function.

The graph represents the sine trigonometric function. This can be determined by observing the shape of the graph, which exhibits the characteristic wave-like pattern of the sine function. The sine function represents the ratio of the length of the side opposite to an angle in a right triangle to the length of the hypotenuse.

The equation x=2cos2x does not represent a graph. It is not possible to have a single equation that represents a graph in this format. Typically, equations that represent graphs involve both x and y variables. Therefore, the statement is false.