A sinusoidal function has an amplitude of 2 units, a period of 180^circ , and a maximum at (0,3) Represent the function with an equation in two different ways.

## Step 1: Determine the general form of the sinusoidal function### Since the function has a maximum at , a cosine function with no phase shift is the simplest choice. The general form is .## Step 2: Determine the amplitude ### The amplitude is given as 2, so .## Step 3: Determine the vertical shift ### The maximum value is 3, and the amplitude is 2. The midline is .## Step 4: Determine the value of ### The period is or radians. The period is related to by Period . Thus, , which gives .## Step 5: Write the first equation### Combining the values of , , and , the first equation is .## Step 6: Write the second equation using a sine function### A cosine function can be represented as a sine function with a phase shift. Since , we can write the second equation as .