Warmup

13-5a Solving Trig Equations Solve Trig equations and identify extraneous solutions

The first step in solving a trigonometric equation is to use factoring, the Zero Product Property, and/or identities to rewrite a complicated equation as a string of simpler trigonometric equations. The second step is to use trigonometric inverses to isolate the variable; that is, to solve an equation such as cos θ = –1, for θ. The third step is to use ideas of periodicity to include all the occurrences of that value.

Infinitely Many Solutions Many trigonometric equations have an infinite number of solutions. If no interval is specified to restrict the number of solutions, the infinite number of solutions must be specified by using an expression rather than by simply using a number. There is a solution that occurs for each full rotation about the origin, a solution has the form a° + k · 360°, where k is any integer.