What Does The Shape Of The Sine Graph Depend On

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. In mathematical terms we say the ‘domain’ of the sine function is the set of all real numbers.

Where does the sine curve come from?

Sine and cosine can be generated by projecting the tip of a vector onto the y-axis and x-axis as the vector rotates about the origin.

What does the amplitude affect on a sine or cosine graph?

The change of amplitude affects the range of the function as well, because the maximum and minimum values of the graph change. Before you multiply a sine or cosine function by 2, for instance, its graph oscillated between –1 and 1; now it moves between –2 and 2. its amplitude is still 5.

How do you describe a sine graph?

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. This graph repeats every 6.28 units or 2 pi radians. It ranges from -1 to 1; half this distance is called the amplitude.

Is a sine graph symmetric?

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.

What does the shape of the sine graph depend on read more >>?

What makes a sine wave?

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 does a affect sine graph?

Clearly we can see the affect a has on the graph y = a sin (bx + c). When 0 < a < 1, the amplitude of the graph decreases, causing the slopes of the graph to appear more “flat”. When a > 1, the amplitude of the graph increases, causing the slopes of the graph to appear more “steep”.

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 is amplitude in a sine graph?

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 does sine look like?

Well, the sine is the length of the side opposite the angle to the length of the hypotenuse. If you think about it (and perhaps draw a picture), you’ll see that since the angle is almost zero the length of the opposite side must also be close to zero.

What are the three characteristics of a sine wave?

Sinusoidal Amplitude, Frequency, and Phase The three characteristics that separate one sinusoid from another are amplitude, frequency, and phase.

Is sine even or odd?

Sine is an odd function, and cosine is an even function. You may not have come across these adjectives “odd” and “even” when applied to functions, but it’s important to know them. A function f is said to be an odd function if for any number x, f(–x) = –f(x).

Is the graph of the sine function symmetric with respect to what?

Sine Function : f(x) = sin (x) symmetry: since sin(-x) = – sin (x) then sin (x) is an odd function and its graph is symmetric with respect to the origin (0 , 0).

What is domain of sine?

Note that the domain of the function y=sin(x) ) is all real numbers (sine is defined for any angle measure), the range is −1≤y≤1 . 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 .

What does sine equal in math?

In a right angled triangle, the sine of an angle is: The length of the side opposite the angle divided by the length of the hypotenuse. The abbreviation is sin. sin θ = opposite / hypotenuse.

What is the period of a sine graph?

What is the period of the sine curve? The period of the sine curve is the length of one cycle of the curve. The natural period of the sine curve is 2π. So, a coefficient of b=1 is equivalent to a period of 2π.

What is the graph of sinx?

The graph of y=sin(x) is like a wave that forever oscillates between -1 and 1, in a shape that repeats itself every 2π units. Specifically, this means that the domain of sin(x) is all real numbers, and the range is [-1,1]. See how we find the graph of y=sin(x) using the unit-circle definition of sin(x).

How is sine curve related to a wave?

How does a sine curve relate to the wave description? A sine curve is a pictorial representation of a wave. Distinguish among these different aspects of a wave: period, amplitude, wavelength, and frequency. Frequency is the number of to-and-fro vibrations it makes in a given time.

What does a sine wave show?

A sine wave or sinusoidal wave is the most natural representation of how many things in nature change state. A sine wave shows how the amplitude of a variable changes with time. The variable could be audible sound for example.

Why are sine graphs useful?

Sine and cosine functions can be used to model many real-life scenarios – radio waves, tides, musical tones, electrical currents.

How do you shape a sine wave?

We can describe the shape of a sine wave by spinning a line around in a circle. The vertical distance from the center of the circle to the tip of the line gives us the amplitude of the sine wave. The faster the line is spinning, the higher the frequency of the resulting sine wave.

How do you shift a sine curve to the right?

By adding or subtracting a number from the angle (variable) in a sine equation, you can move the curve to the left or right of its usual position. A shift, or translation, of 90 degrees can change the sine curve to the cosine curve.