Modeling with Trig. Functions

After completing the previous sections on Trigonometric Functions, we are almost ready to try and work on "real world" problems. But before getting to that, lets recall the sine graph:

sine graph

We recall from the section More Trig. Functions that the period, T, of the sine curve is 2pi. If we wanted to know the FREQUENCY (denoted by f) - which is the number of times the curve oscillates in 1 second - we use the formula: f = 1/T. From the graph we see that the sine curve oscillates between 1 and -1. From this, we determine the AMPLITUDE to be 1. (We determine this by subtracting the lowest point from the highest point and then dividing by 2. ie: (1 - (-1))/2 = 2/2 = 1.) The last thing we must note is the Angular Velocity. This is the number of radians (or degrees) an angle can move through in 1 second. Angular velocity, b, is given by the formula: b = Angle(x)/time(t).

We are now ready to look at some examples.

Introductory Exercises Moderate Exercises