Show Your Skills!
Use your graphing utility and the techniques you have learned to solve each of these problems on your own.
A nail is stuck in a car's tire. The position of the nail with respect to the ground (in inches) is represented by the function \( y = - 18\cos{\left( 2x \right) +}18 \), with time in \( x \) seconds. When does the nail reach a height of 34 inches on the interval \( 0 < x < 4 \)?
The nail reaches a height of 34 inches off the ground at 1.33 seconds and 1.809 seconds during the interval from 0 to 4 seconds.
The position of a rung on a waterwheel in feet above water level is represented by the function \( y = - 18\sin{\left( \frac{\pi}{6}x \right) +}12 \), with time in \( x \) seconds on the interval \( 0 < x < 10 \). When is the rung 4 feet under water?
The rung is 4 feet underwater at 2.091 and 3.909 seconds.
The depth of ocean waves in feet can be represented by the function \( y = - 4\cos{\left( \frac{\pi}{12}\left( x - 3 \right) \right) +}8 \), with time in \( x \) hours on the interval \( 0 < x < 24 \). When are the waves 10 feet high?
The waves are 10 feet high after 11 hours and 19 hours.
The height of ocean tides can be represented by the function \( y = 10\sin{\left( \frac{\pi}{8}(x - 4) \right) +}16 \), with time in \( x \) hours. Graph the function using a graphing utility on the interval \( 0 < x < 24 \). When is the tide 20 feet high?
The tide is 20 feet high after 5.048, 10.952, and 21.048 hours.
