Question

The graphs of sinusoidal functions (sine and cosine) have top (maximum) points, bottom (minimum) points, and middle (with respect to the range) points. It is useful when graphing or writing equations for transformations of sine and cosine graphs to think about at which of these points the functions begins (i.e. the value of the parent function when x 0) and if the function increases or decreases from that point. For example, the graph of f(x) = cos(x) starts at the top and decreases. For each function below, decide where it starts and if it increases or decreases from that point. a. f(x) = sin(x)b. f(x) = - cos(x)c. f(x) = - sin(x) hp

Answer 1

(a)

The image below shows the graph of f(x) = sin(x).

As you can observe in the image above, the sine function starts at the middle (origin) and increases from that point to (pi/2, 1), which is a maximum.

(b)

The image below shows the graph of f(x) = -cos(x).

As you can observe in the image above, function b begins at the bottom and increases.

(c)

The image below shows the graph of the function f(x) = -sin(x).

This function starts at the middle and decreases.