Trigonometric Equations and Inequalities
Trig equations come with built-in multiplicity: the inverse function contributes one solution, symmetry contributes the partner (pi minus the angle for sine, the negative for cosine, a pi-step for tangent), and periodicity multiplies both into infinite families that a stated domain then filters. Completeness is the skill: exactly the right solutions, no more, no fewer.
Solutions are lost three ways: keeping only the inverse’s single answer, dividing both sides by a trig factor that can be zero (factor instead), and solving a transformed argument like sin 2x in an unwidened window. They are invented two ways: partner formulas misapplied, and calculators left in degree mode. All five failures are drilled in the lesson.
The work
3 ways in · any order
Lesson
Trigonometric Equations and Inequalities
›
One from the inverse, one from symmetry, the family from periodicity: the lesson builds complete solution sets, enforces factor-never-divide, widens windows for transformed arguments, and keeps the calculator honest in radians. Ten scenarios audit completeness every way it fails.
Diagnostic
10-item topic check
›
Ten items spanning the three Topic 3.10 misconceptions: solutions lost to division or unwidened windows, partners misplaced or missing, and degree-mode contamination. Results route you to the drills that fix what fired.
Targeted Practice
Drill a single misconception
›
Pick one of the failure modes you missed and drill it on its own. The round is adaptive: two correct in a row clears the misconception and moves you to the next.