Lesson 2

Lesson 2 Summary

 

In this lesson you learned that, with the exception of sin θ = ±1 and cos θ = −1, all equations of the form cos θ = k, where −1 ≤ k ≤ 1, have two solutions when angles are limited to 0° ≤ θ ≤ 360°.

 

You learned about each type of equation.

 

Sine: sin θ = k, where −1 ≤ k ≤ 1

• The first solution, θ1, can be obtained by entering sin−1(k) in your calculator.
  
  
• The second solution will have a terminal arm that is a reflection in the y-axis of θ1’s terminal arm.
  
  
• Your calculator may give you a negative angle. This negative angle corresponds to a clockwise rotation and can be converted to a positive angle using 360° − θ1.

Cosine: cos θ = k, where −1 ≤ k ≤ 1

• The first solution, θ1, can be obtained by entering cos−1(k) in your calculator.
  
  
• The second solution will have a terminal arm that is a reflection in the x-axis of θ1’s terminal arm.

Tangent: tan θ = a, a ∈

• The first solution, θ1, can be obtained by entering tan−1(k) in your calculator.
  
  
• The second solution will have a terminal arm that is a reflection in the x-axis and y-axis of θ1’s terminal arm. As a result, the two terminal arms form a straight line.

In all cases, circle symmetry was used to determine the second solution.