Solve each equation on the interval

Question

0 less than or equal to theta less than or equal to 2pi

cos(theta)=1/2

cos(theta)=-square root 3/2

Answer 1

Think about where on the unit circle cosine is equal to 1/2. Cosine is positive in Quadrant I and Quadrant IV. In Quadrant I, cosine is 1/2 at π/3. Reflect that angle over the x-axis to find the point in Quadrant IV with cosine 1/2: (5π)/3.

 

Think about where on the unit circle cosine is equal to -√(3)/2. Cosine is negative in Quadrant II and Quadrant III. In Quadrant I, cosine is √(3)/2 at π/6. Reflect that angle over the y-axis to find the point in Quadrant II with cosine -√(3)/2: (5π)/6. Reflect that angle over the x-axis to find the point in Quadrant III with cosine -√(3)/2: (7π)/6.