### 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?

( HINT , SOLUTION )

(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?

( HINT , SOLUTION )