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
- What is the period of the oscillation?
- What does Vo represent?
- Sketch the graph of V against t. (Take Vo to be some unknown positive quantity.) Label the axes.
- If Vo is 0.5 volts, what is the voltage at time t = 30?
- If Vo is 0.5 volts, what is the first time when the voltage is 0.25 volts?
(2) A population of animals varies sinusoidally between a low of 700 on January 1 and a high of 900 on July 1.
- Graph the population against time.
- Find a formula for the population as a function of time, t, measured in months since the start of the year.
- 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?