What is the amplitude of a cosine function?

Amplitude and Period a Cosine Function The amplitude of the graph of y=acos(bx) is the amount by which it varies above and below the x -axis. Amplitude = | a | The period of a cosine function is the length of the shortest interval on the x -axis over which the graph repeats. Period = 2π|b|

What is the amplitude of the cosine wave?

The amplitude of the sine and cosine functions is the vertical distance between the sinusoidal axis and the maximum or minimum value of the function.

What is the amplitude of the graphs of the sine and cosine functions?

The amplitude of y=asin(x) and y=acos(x) represents half the distance between the maximum and minimum values of the function. Example: Find the period and amplitude of y=52cos(x4) .

What is the difference between a sine and cosine graph?

The basic sine and cosine functions have a period of 2π. The function sin x is odd, so its graph is symmetric about the origin. The function cos x is even, so its graph is symmetric about the y-axis. The graph of a sinusoidal function has the same general shape as a sine or cosine function.

What is the cosine function equation?

The cosine function is expressed as f(x) = Acos(Bx + C) + D where A, B, C, and D are numbers, and the periods of these cosine functions differ.

What’s the amplitude of a sine graph?

The amplitude of the sine function is the distance from the middle value or line running through the graph up to the highest point. In other words, the amplitude is half the distance from the lowest value to the highest value.

What type of functions are sine and cosine?

The trigonometric functions cos and sin are defined, respectively, as the x- and y-coordinate values of point A.

Is cos a real function?

The graph of the cosine function looks like this: The domain of the function y=cos(x) is all real numbers (cosine is defined for any angle measure), the range is −1≤y≤1 .

Is the amplitude of a function always positive?

Amplitudes are always positive numbers (for example: 3.5, 1, 120) and are never negative (for example: -3.5, -1, -120). Amplitudes are positive because distance can only be greater than zero or equal to zero; negative distance does not exist.

How do you find the amplitude of sin and cosine?

Amplitude and Period of Sine and Cosine Functions The amplitude of y = a sin ( x ) and y = a cos ( x ) represents half the distance between the maximum and minimum values of the function.

How do you find the amplitude of a function?

The amplitude of y = a sin ( x) and y = a cos ( x) represents half the distance between the maximum and minimum values of the function. Let b be a real number.

What is the maximum value of a cos?

Similarly, the maximum value of A cos is A. The absolute value of A is called the amplitude of the functions y A sin and y A cos. The amplitude can also be described as the absolute value of one-half the difference of the maximum and minimum function values.

What is the amplitude of Y/4 Cos?

According to the definition of amplitude, the amplitude of y A cos is A . So the amplitude of y 4 cos is 4 or 4. 368Chapter 6 Graphs of Trigonometric Functions