SOLVE AND GRAPH EACH PROBLEM.

1.)Graph y = 2cos 2x by following the steps below. (3 points)

Step 1. Identify Aand Bin y = 2cos 2x.

A =

B =

Step 2:Calculate the amplitude and period of y = 2cos 2x.

Amplitude =

Period =

Step 3: Graph y = 2cos 2xon the coordinate grid below from x = 0 to x = 2.

.

2.) Graph by following the steps below. (3 points)

Step 1.A phase shift has been added to y = 2cos 2x.Calculate the phase shift using the formula:

Phase Shift = =

Step 2: Graph on the coordinate grid below from x = 0 to x = 2.

3.) Graph by following the steps below. (3 points)

Step 1. Graph on thecoordinate grid on the next page, from x = 0 to x = 2, using a dotted curve as a guideline for graphing the secant graph.

Step 2: Draw in the asymptotes for .

Step 3: Graph on the same coordinate grid below from x = 0 to x = 2.

4.) Mickey's fun wheel ride is a giant Ferris wheel with a radius of 76 feet and it rotates a full revolution in 2 minutes. A gondola starts at the lowest point on the wheel which is 2 feet above the ground at t = 0. Write and graph a sinusoidal equation model for the height, h, in feet, of the gondola as a function of time, t, in minutes. (6 points)

Step 1.Find the midpoint between the minimum and maximum values to find the midline. Show your work.

Midpoint =

Midline h =

Step 2:Calculate the amplitude and the value of B for the equation Show your work.

Amplitude =

B =

Step 3: Write the sinusoidal curve equation that models the data

h =

Step 4: Label the intervals on the x-axis and y-axis and graph the sinusoidal curve equation.