Try This 3

1. Solve the equation 2 cos θ + 1 = 0, 0° ≤ θ < 360°. Record the two solutions in a table similar to the table shown.
2. Use Coterminal Angles 2 to find all the coterminal angles for each solution from −720° to 1080°, and complete the table.
   
   
    
   
   

3. Replace θ from the original equation with one of the coterminal angles you found in question 2. Simplify. What do you notice? Is this true for all of the coterminal angles?

4. Use your results from question 3 to determine all solutions to 2 cos θ + 1 = 0, −720° ≤ θ < 1080°.

5. How many solutions will there be to 2 cos θ + 1 = 0 if the domain is the real numbers instead of −720° ≤ θ < 1080°?

6. How could you represent all the solutions over the real numbers?

7. Repeat questions 1 to 6 using the equation tan θ − 1 = 0 with radians instead of degrees.

Save your responses in your course folder.

Share 3

With a partner or group, discuss the following questions based on your results from Try This 3.

1. How were you able to represent all the solutions to the two equations over the real numbers? Were your methods different?
2. Why could the solutions to the tangent equation be shown using one expression while the solutions to the cosine equation required two expressions?

If required, save a record of your discussion in your course folder.