Question

Provide an example of a trig function that includes multiple transformations. Describe how it is different from the standard trig function f(x) = sin x, f(x) = cos x, or f(x) = tan x using key features.

1. thienthi
An example of a trig function that includes multiple transformations and how it is different from the standard trig function is; As detailed below

### How to interpret trigonometric functions in transformations?

An example of a trigonometric function that includes multiple transformations is; f(x) = 3tan(x – 4) + 3
This is different from the standard function, f(x) = tan x because it has a vertical stretch of 3 units and a horizontal translation to the right by 4 units, and a vertical translation upwards by 3.
Another way to look at it is by;
Let us use the function f(x) = sin x.
Thus, the new function would be written as;
g(x) = sin (x – π/2), and this gives us;
g(x) = sin x cos π/2 – (cos x sin π/2)  = -cos x
This will make a graph by shifting the graph of sin x π/2 units to the right side.
Now, shifting the graph of sin xπ/2 units to the left gives;
h(x) = sin (x + π/2/2)