Quadratic Trigonometric Equations (Edexcel A-Level Mathematics): Flashcards

$a \cdot (\text{trig function})^2 + b \cdot (\text{trig function}) + c = 0$

Use substitution, rearrangement, and factoring techniques.

$u = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Replace $u$ with the original trigonometric function.

Typically $0°$ to $360°$ or $0$ to $2\pi$ radians.

$\theta = 210°$ or $\theta = 330°$.

$\cos(\theta)$ must be between $-1$ and $1$.

$\theta = 90° + 180°k$, where $k$ is any integer.

$\theta = 60°, 120°, 240°, 300°$.

Use quadratic formula and check valid cos values.