# Why is the graph of sine a wave?

Space and AstronomyThe 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]**.

## Why is sine a wave?

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.

## What is a sine wave graph?

To graph the sine function, we mark the angle along the horizontal x axis, and for each angle, we put the sine of that angle on the vertical y-axis. The result, as seen above, is **a smooth curve that varies from +1 to -1**. Curves that follow this shape are called ‘sinusoidal’ after the name of the sine function.

## Is a sine curve related to a wave?

**A sine curve is related to a wave by the shape of its graph and by its periodic properties**.

## Why is a sine graph curved?

Video quote: *Okay that's where it gets this shape from that's where it gets its name from rubber. So it's a smooth curve.*

## Why is a sine graph smooth?

The graph of sine function is smooth because **it is defined for all real values of x and it is differentiable at every x**. So as a result graph is continuous and is periodic (having a period of 2pie) . As the graph is continuous and graph is repeated after a certain interval it is a periodic function.

## Can you rotate a sine graph?

Video quote: *In my tutorial that i mentioned. But for now i'm just going to have a slider here for the a and you'll notice that i can rotate my graph.*

## How do you rotate on a graph?

Video quote: *How you could rotate a curve 90 degrees just by swapping the y's and x's around and how changing the signs of the X's from positive to negative would rotate the curve 180 degrees.*

## How do you rotate a line on a graph?

Video quote: *The way you can find out what this point is is by setting the y-value equal to 0 because when you're crossing the x-axis you're not going up or down we know that the y-value is 0.*

## How do you change the angle of a sine wave?

You can move a sine curve up or down by simply **adding or subtracting a number from the equation of the curve**. For example, the graph of y = sin x + 4 moves the whole curve up 4 units, with the sine curve crossing back and forth over the line y = 4.

## How do you graph a sine function?

Video quote: *So 2 PI over B is equal to 8 which means that B is PI over 4 the next thing that I want to do is choose a starting point so I'm going to start right there on the y axis. It's an intercept.*

## How do you move a sine graph to the right?

**Shift the graph horizontally**. To find the new starting place, set what’s inside the parentheses equal to the starting value of the parent graph: The figure shows what you have so far. Shifting the parent graph of y = sin x to the right by pi/4.

## How do you change a sine graph to horizontal?

the horizontal shift is obtained by **determining the change being made to the x-value**. 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.

## What is the phase shift of a sine graph?

Phase Shift is **a shift when the graph of the sine function and cosine function is shifted left or right from their usual position** or we can say that in phase shift the function is shifted horizontally how far from the usual position. Generally, functions are shifted (π/2) from the usual position.

## Is sine horizontal or vertical?

In the diagram shown, as sin function is opposite side/ Hypotenuse, we find the horizontal component as sin function. In this diagram, we find sin function to be the **vertical component** because of the angle orientation.

## How do you change a sine wave into a cosine wave?

Video quote: *So time period is 2pi. If you are working in radians or it all depends right let's say we are working in radians then it'd be two pi PI K. Right. So the quarter cycle.*

## How do you change a sine graph into a cosine graph?

Video quote: *So if I move a sine graph a quarter of the period across to the left it's going to become a cos curve.*

## How do I know if a graph is sine or cosine?

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

## How do you go from sine to cosine graph?

**Translating Sine and Cosine Functions**

- The general equation for a sine and cosine curve is y=Asin(x−h)+k and y=Acos(x−h)+k,respectively. …
- Graph y=sin(x+2)+3.
- Step 3: The horizontal shift is the hardest to find. …
- Graph the following functions on [−π,3π]:
- y=−1+sinx.
- Graph y=cos(x+π3)−2.

## Where does a sine graph start?

The Sine Function has this beautiful up-down curve (which repeats every 2π radians, or 360°). It **starts at 0**, heads up to 1 by π/2 radians (90°) and then heads down to −1.

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