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How do you find the transformation of a sine function?

How do you find the transformation of a sine function?

Graphing f(x) = cos(x) is another way to create a wave. A cosine graph is a transformation of a sine graph. While f(x) = sin(x) starts at the axis of the curve, f(x) = cos(x) starts at is maximum value. For any sinusoidal function, there is both a sine and cosine equation.

What does the sine graph represent?

The graphs of functions defined by y = sin x are called sine waves or sinusoidal waves. Notice that the graph repeats itself as it moves along the x-axis. The cycles of this regular repeating are called periods. This graph repeats every 6.28 units or 2 pi radians.

What does a sine curve look like?

The shape of the sine curve is the same for each full rotation of the angle and so the function is called ‘periodic’. The period of the function is 360° or 2π radians. You can rotate the point as many times as you like. This means you can find the sine of any angle, no matter how large.

What is the difference between sine and cosine transformations?

As was said in comments, cosines and sines differ only by phase shift. The difference in their performance arises from their boundary behavior. On an interval [0,ℓ], the sine system {sin2πnℓ} satisfies the Dirichlet boundary condition, attaining zero value at 0,ℓ.

What are the key features of a sine graph?

The sine and cosine functions have several distinct characteristics:

  • They are periodic functions with a period of.
  • The domain of each function is ( − ∞ , ∞ ) and the range is.
  • The graph of y = sin x y = sin x is symmetric about the origin, because it is an odd function.

How do you describe a sine curve?

A sine wave is a geometric waveform that oscillates (moves up, down or side-to-side) periodically, and is defined by the function y = sin x. In other words, it is an s-shaped, smooth wave that oscillates above and below zero.

How do you tell if a graph is sine or cosine?

Comparing Cosine and Sine Functions in a Graph

  1. Replace cos x with its cofunction identity.
  2. Apply the two identities for the sine of the sum and difference of two angles. The two identities are.
  3. Simplify the terms by using the values of the functions. So you see, the shifted sine graph is equal to the cosine graph.

What does a cos graph look like?

To graph the cosine function, we mark the angle along the horizontal x axis, and for each angle, we put the cosine of that angle on the vertical y-axis. The result, as seen above, is a smooth curve that varies from +1 to -1. It is the same shape as the cosine function but displaced to the left 90°.

Why do sine waves have a curved shape?

How do you go from sin to cos?

All triangles have 3 angles that add to 180 degrees. Therefore, if one angle is 90 degrees we can figure out Sin Theta = Cos (90 – Theta) and Cos Theta = Sin (90 – Theta).

What are the 5 key points of sine?

They are the three x-intercepts, the maximum point, and the minimum point. All of these are on your unit circle. The values of sin x correspond to the y-values, so those key points are (angle, y-value) or (0,0), (π/2, 1), (π, 0), (3π/2, -1), (2π, 0).

What is the equation for a sine graph?

The general equation of a sine graph is y = A sin(B(x – D)) + C. The general equation of a cosine graph is y = A cos(B(x – D)) + C. Example: Given a transformed graph of sine or cosine, determine a possible equation.

What is the formula for vertical translation?

For an equation: A vertical translation is of the form: #y = sin(theta) + A# where # A!=0#. OR #y = cos(theta) + A#. Example: #y = sin(theta) + 5# is a #sin# graph that has been shifted up by 5 units.

How do you calculate horizontal shift?

The horizontal shift is C. The easiest way to determine horizontal shift is to determine by how many units the “starting point” (0,0) of a standard sine curve, y = sin ( x ), has moved to the right or left. Horizontal shifts can be applied to all trigonometric functions.

What is a sin function graph?

A sine graph is a graph displaying the function of y = sin x. A sine graph has a function which may also be described as a sinusoidal wave. It repeats itself as it moves along the x-axis, and the cycle taken for a repetition is known as the period of the sine graph.