MODERATE EXERCISES - Modeling with Trigonometric Functions

(1) The voltage, V, of an electrical outlet in a home is given as a function of time, t (in seconds), by

V = Vo cos(120 t).
  1. What is the period of the oscillation?
  2. What does Vo represent?
  3. Sketch the graph of V against t. (Take Vo to be some unknown positive quantity.) Label the axes.
  4. If Vo is 0.5 volts, what is the voltage at time t = 30?
  5. If Vo is 0.5 volts, what is the first time when the voltage is 0.25 volts?

( Click On HINT To Get Some Help , Click On SOLUTION To See The Answer )

(2) A population of animals varies sinusoidally between a low of 700 on January 1 and a high of 900 on July 1.

  1. Graph the population against time.
  2. Find a formula for the population as a function of time, t, measured in months since the start of the year.
  3. According to your formula, what is the population on March 15?


(3) A child is swinging on a garden swing with supporting rope lengths of 3.5 m. When the swing angle (with respect to the vertical) is 30o, how high is the child compared with her lowest position?


Introductory Exercises Moderate Exercises