1.5.5—Trig equations

Solve a trig equation by reducing it to a principal angle, applying quadrant symmetry, then adding periods. The interval determines which solutions survive.

Factorise or use a substitution when expressions such as 2sin²x−sinx−1 appear. Check every candidate in the original equation, especially after squaring.

2sinx−1=0 gives sinx=1/2, so on [0,2π] the solutions are π/6 and 5π/6.

One inverse-trig answer is not the complete solution, and the period of tan is π rather than 2π.