Consider the general form of a transformed cosine function, y=acos b(x-h)+k.
Practice makes perfect
Let's consider the given function.
y=-2cos(x-π/3)-4
Now we will compare our function with the general form of a transformed cosine function.
General Form
y= a cos b(x- h)+ k
Given Function
y= -2 cos 1 ( x- π/3 )+( - 4)
Because a= -2 and b= 1, the desired graph is a translation of y= -2cos x. This is a reflection across the x-axis followed by a vertical stretch of the graph of its parent function, y=cos x, by a factor of 2. Let's sketch one cycle of this function.
Since k= - 4, the graph of the given function translates the graph of y=-2cos x down by 4 units. The horizontal translation of a periodic function is called a phase shift. Therefore, h= - π3 tells us that there is a phase shift of π3 units to the right.
Finally, we will draw the obtained graph in the interval from 0 to 2π. We will extend the current pattern to 0 and restrict the domain to values of x that are not greater than 2π.
