Solve cos(2t) = 1/2 on the interval from 0 to 2 pi.

1. Cosine equals 1/2 in quadrants I and IV, so the doubled angle 2t equals pi/3 or 5 pi/3. 2. Halving those gives t = pi/6 and t = 5 pi/6. 3. Because t runs to 2 pi, the doubled angle runs to 4 pi, so another turn must be checked. 4. Adding 2 pi to pi/3 gives 7 pi/3, and halving gives t = 7 pi/6. 5. Adding 2 pi to 5 pi/3 gives 11 pi/3, and halving gives t = 11 pi/6. 6. One further turn gives 13 pi/3 and 17 pi/3, whose halves 13 pi/6 and 17 pi/6 exceed 2 pi and are rejected. 7. The four solutions are pi/6, 5 pi/6, 7 pi/6 and 11 pi/6. 8. Stopping after the first turn would return only two of them, which is the usual error with a compressed argument. _Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 9 "Trigonometric Identities and Equations", section 9.5 Solving Trigonometric Equations_