FST 4.5 Sine and Cosine Graphs

The amplitude is the maximum distance from the midline to the peak (or trough) of the graph. It represents half the distance between the maximum and minimum values.

The amplitude is 3, which is the coefficient in front of the sine function.

The period is the distance along the x-axis for one complete cycle of the graph. For the function y = sin(kx), the period is given by $$\frac{2\text{π}}{k}$$ .

The period is $$\frac{2\text{π}}{2} = \text{π}$$ .

The maximum value is 4 and the minimum value is -4.

The midline is y = 0, which is the horizontal line that runs through the middle of the graph.

At x = 90 degrees, the coordinates are (90, 1) because sin(90°) = 1.

The amplitude is 2, calculated as $$\frac{2 - (-2)}{2} = 2$$ .

The frequency is $$\frac{1}{\text{Period}} = \frac{1}{4}$$ .

Increasing the amplitude stretches the graph vertically, making the peaks and troughs higher and lower, respectively.