Feb 27, 2025 · The amplitude of a trigonometric function refers to the height of its peaks (highest points) or the depth of its troughs (lowest points) relative to its midline, also known as the …

Use the form acos(bx−c)+ d a cos (b x - c) + d to find the variables used to find the amplitude, period, phase shift, and vertical shift. Find the amplitude |a| | a |. Find the period of cos(x) cos …

Mar 1, 2025 · Amplitude is the vertical distance between the sinusoidal axis and the maximum or minimum value of a sine or cosine function. The general form of a sinusoidal function is f ( x ) = …

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. Amplitude = | a | Let b be a real number.

The amplitudes of the basic trigonometric functions are as follows: \[\begin{array}{|c|c|} \hline \text{Function} & \text{Amplitude}\\ \hline \sin (\theta) , \cos( \theta ) &1 \\ \hline \csc (\theta) , …

The absolute value of A is called the amplitude of. A sin and y A cos . The amplitude of the functions y value of A, or A . The amplitude can also be described as the absolute value of one-half the difference of the maximum and minimum function values. 1 a. State the amplitude for the function y. b. Graph y. c. Compare the graphs. 4 cos .

Oct 17, 2024 · Amplitude of Cosine Function. Amplitude: 1; Period: 2π; Like the sine function, the cosine function also oscillates between -1 and 1, repeating every 2π. The main difference is …

Sinusoidal functions (or sinusoid ∿) are based on the sine or cosine functions. y = A ⋅sin(ωx+ϕ) y = A ⋅ sin (ω x + ϕ) y = A ⋅cos(ωx+ ϕ) y = A ⋅ cos (ω x + ϕ) where A is the amplitude, ω (omega) …

Amplitude and Period a Cosine Function. The amplitude of the graph of y = a cos ( b x ) 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 …

How to Determine Amplitude and Period Length for Sine and Cosine Functions Example 1 a. State the amplitude for the function y = 3 cos . b. Graph y = 3 cos and y = cos on the same set …

Mar 1, 2025 · Graph the following function by plotting main points: f (x) = − 2 ⋅ cos x. The amplitude is 2, which means the maximum values will be at 2 and the minimum values will be …

Free practice questions for Precalculus - Find the Amplitude of a Sine or Cosine Function. Includes full solutions and score reporting.

Find the amplitude of the function f(x) = − 3cosx and use the language of transformations to describe how the graph is related to the parent function y = cosx. The new function is reflected …

Mar 31, 2025 · The Y cos X graph exhibits several important properties, including: Periodicity: The graph is periodic with a period of 2π, meaning it repeats every 2π units. Amplitude: The …

A periodic function is one which repeats itself over and over in horizontal direction. What is period ? The period of a periodic function is the length of one repetition or cycle. What is amplitude ? …

Many real-life problems can be solved by applying trigonometric functions, such as sine, cosine, and tangent. This lesson will define these functions, show how to graph them using their …