How well do you know Amplitude and Period?

The amplitude of a sine function is the distance between the maximum and minimum values of the function. In this case, the coefficient in front of the sine function is 3, which represents the amplitude. Therefore, the amplitude of y=3sin(7x)-2 is 3.

The value "a" represents the amplitude in the function y = a sin(bx-h) + k. Amplitude refers to the maximum displacement or distance from the equilibrium position in a periodic function. In this case, "a" determines the vertical stretch or compression of the graph, indicating how high or low the function will oscillate from the midline.

The amplitude of a function measures the distance from the midline (or average value) of the function to its maximum or minimum value. It represents the maximum displacement of the function from its midline.

The horizontal length required to complete one cycle is called the period. The period represents the time it takes for a complete oscillation or vibration to occur. It is often measured in seconds and is a fundamental concept in the study of waves and oscillations. The period is inversely related to the frequency of the wave, meaning that a shorter period corresponds to a higher frequency and vice versa.

The amplitude of a sinusoidal function determines the maximum distance the graph reaches from its midline. In this case, the amplitude is 2, indicating that the graph oscillates between a maximum value of 2 and a minimum value of -2.

The period of a sinusoidal function is the distance between two consecutive peaks or troughs of the graph. In this case, the period is 2π, which means that the graph completes one full cycle every 2π units.

Therefore, the correct answer is A = 2, P = 2π.

The normal period of a sine or cosine function is 2π. This means that the graph of the function repeats itself every 2π units along the x-axis.

The period of a sine or cosine graph can be found by dividing 2π by the coefficient of the variable inside the trigonometric function. In this case, the coefficient is B, so the period would be 2π/B.

The equation for a sine function with an amplitude of 6 and a period of π/4 is y=6sin(8x). The amplitude of 6 means that the graph will oscillate between -6 and 6. The period of π/4 means that the graph will complete one full cycle in a distance of π/4 on the x-axis. The coefficient of 8 in front of x indicates that the graph will be compressed horizontally, making it oscillate more rapidly.

To convert degrees to radians, we use the formula: radians = (degrees * π) / 180. In this case, we have 100 degrees. Plugging this value into the formula, we get: radians = (100 * π) / 180 = 5π/9. Therefore, the correct answer is 5π/9.

The given equation is in the form y = A*sin(Bx), where A represents the amplitude and B represents the period. In this case, the amplitude is 2, which represents the maximum value that the function reaches above and below the x-axis. The period is also 2, which represents the distance between two consecutive peaks or troughs of the graph.