Applications of Sinusoidal Functions

When solving problems that involve periodic (sinusoidal) function, a good procedure to follow is:

Draw a rough graph by plotting the points and sketching a curve of best fit

Write an algebraic equation that represents the sinusoidal graph. The equation should be in the form:y = a sin b(x + c) + d

Use the equation to find any required values or information

Example 1: A water wheel with a 7.0 ft radius has 1.0 ft. submerged in the water as shown, and rotates counterclockwise at 6.0 revolutions per minute. A bug is sitting on the wheel at point B. You start your stopwatch, and two seconds later the bug at point B is at its greatest height above the water. You are to model the distance 'h' of the bug from the surface of the water in terms of the number of seconds 't' the stopwatch reads.