Transformations of Trigonometric Functions HW

The midline is the horizontal line that runs through the middle of the graph of a trigonometric function, determined by the value of k in the equation $$y=a\text{sin}(b(x-h))+k$$ .

The parameter k affects the midline.

The phase shift is found by identifying the value of h in the function $$y=\text{cos}(b(x-h))$$ , where the phase shift is $$h$$ units to the right if h is positive and to the left if h is negative.

The phase shift is $$\frac{\text{π}}{2}$$ to the right.

The period is calculated as $$\frac{2\text{π}}{|b|}$$ .

The period is $$3\text{π}$$ .

The vertical shift indicates how much the graph is moved up or down, determined by the value of k in the equation $$y=a\text{sin}(b(x-h))+k$$ .

The vertical shift is down 4.

The amplitude is the maximum distance from the midline to the peak (or trough) of the graph, determined by the absolute value of a in the equation $$y=a\text{sin}(b(x-h))+k$$ .

The amplitude is 3.