Solving 2sin²θ - sinθ - 1 = 0

Algebra 2 · Axiom Academy

Treat as the variable in a quadratic, factor it, then solve on . Solve for all in by treating as the variable in a quadratic equation. Nice work — you solved a trig equation by recognizing its hidden quadratic shape. Here's what to remember: Spot the quadratic shape: an equation where (or , ) appears squared and to the first power factors just like a polynomial, once you substitute . Factor and solve for u first: only substitute back to once the algebra is finished. Count solutions carefully: contributes only ONE angle on — it's the unique maximum of sine — while a generic value like contributes two. Result: the complete solution set is . This substitute → factor → back-substitute → unit-circle strategy solves any trig equation that's secretly a polynomial in disguise.

This is the written version of the interactive lesson above. See the full Algebra 2 course.