Chapter 10 - NCPN

As a paddle wheel spins on its axis, the height
of a point on the wheel with respect to the
water level can be modeled by the function
h(t) = 15 – 18cos ≠t . The height above
12
or below the water is given in feet, and t is
the amount of time in seconds. Answer the
following questions to describe the paddle
wheel as it spins on its axis.
a. What is the diameter of the wheel
b. How high above the surface of the water is
the top of the wheel
c. How long does it take the wheel to complete
one full revolution
Step 1 Understand the Problem
Describe the problem situation in your own
words. What information do you need to find
Step 2 Develop a Plan
Problem-solving strategy: Use a graph.
What are suitable axis limits to graph the
cosine function How will graphing the
function help you answer the questions in
the problem statement
Step 3 Carry Out the Plan
Graph the trigonometric function on a graphing
calculator or on grid paper using suitable axes.
Use the graph to find the diameter of the
wheel, the maximum height above the surface
of the water, and the amount of time it takes
to complete a full revolution. Explain how you
found your answers.
Step 4 Check the Results
Check your results to make sure they
seem reasonable.
Lesson Assessment
Think and Discuss
1. Explain how to solve the equation cos 2 θ – 1 = 0 for 0 ≤ θ < 180°.
2. How many solutions are there to the equation 4 tan θ – 0.25 = 0
Explain.
3. If the sine of an angle is positive and one of the solutions in
the interval 0 ≤ θ < 2π is known, how can the other solution
be found
4. How could a graphing calculator be used to find the solutions of
a trigonometric equation within a particular domain
488 Chapter 10 Trigonometric Functions and Identities