## What is the transformation of the sine equation?

Using Transformations of Sine and Cosine Functions Sketch a graph of the y-coordinate of the point as a function of the angle of rotation. Recall that, for a point on a circle of radius r, the y-coordinate of the point is y=rsin(x), so in this case, we get the equation y(x)=3sin(x).

## What are the transformations of sinusoidal functions?

Transformations are applied until the behaviour can be described by a particular function. Transformations can be combined to produce more complex sinusoidal functions. a phase shift (horizontal translation) of c, • its axis (vertical translation) at y = d, • a minimum value of d − |a|, • a maximum value of d + |a|.

**How are sine and cosine graphs different?**

In a cosine graph, a positive or negative number vertically flips the graph and determines whether the graph starts at the maximum (if it’s positive) or minimum (if it’s negative). For a sine graph, a positive or negative number vertically flips the graph like it does with a cosine graph.

### How do you transform a trig graph?

The transformation y = af(x) is a vertical stretch of y = f(x) with scale factor a parallel to the y-axis. The transformation y = –af(x) is a vertical stretch of y = f(x) with scale factor a parallel to the y-axis and then a reflection in the x-axis.

### What are transformations of trigonometric?

The graphs of the six basic trigonometric functions can be transformed by adjusting their amplitude, period, phase shift, and vertical shift. Amplitude. The amplitude of a sinusoidal trig function (sine or cosine) is it’s ‘height,’ the distance from the average value of the curve to its maximum (or minimum) value.

**Where do sin and cos graphs intersect?**

The graphs intersect at about −0.7854 or − and about 2.356 or . Therefore, on –π < x < π, –sin x = cos x when x = − and .

## How do you find the transformation of a trig function?

The phase shift of a trigonometric function is calculated using the formula phase shift=CB phase shift = C B When C is positive, the graph will appear to shift to the right. When C is negative, the graph will shift to the left. Adding a value D to a trig function will translate its graph vertically.

## How are the graphs of sine and cosine related?

The graphs of sine and cosine have the same shape: a repeating “hill and valley” pattern over an interval on the horizontal axis that has a length of . The sine and cosine functions have the same domain—the real numbers—and the same range—the interval of values .

**How would you describe the graphs of the sine and cosine functions?**

The graph of y = sin x y = sin x is symmetric about the origin, because it is an odd function. The graph of y = cos x y = cos x is symmetric about the y -axis, because it is an even function.

### How do you change a sine graph?

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.

### What is the rule for the transformation?

What is the Rule for the Transformations? Suppose a parent function is f(x), f(x)+a shifts f(x) up by a units, f(x+a) shifts f(x) left by a units, -f(x) reflects f(x) over the x-axis, f(-x) reflects f(x) over the y-axis, a. f(x) stretches or shrinks f(x) vertically and f(a.x) stretches or shrinks f(x) horizontally.

**How do you graph transformations?**

5 Steps To Graph Function Transformations In Algebra

- Identify The Parent Function.
- Reflect Over X-Axis or Y-Axis.
- Shift (Translate) Vertically or Horizontally.
- Vertical and Horizontal Stretches/Compressions.
- Plug in a couple of your coordinates into the parent function to double check your work.