| Exam Board | WJEC |
|---|---|
| Module | Unit 3 (Unit 3) |
| Year | 2018 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Quadratic trigonometric equations |
| Type | Show then solve: secant/cosecant/cotangent identities |
| Difficulty | Standard +0.8 This trigonometric equation requires recognizing the identity sec²θ = 1 + tan²θ to convert to a single-variable quadratic, then solving for tan θ and finding all solutions in the given range. It's above average difficulty due to the identity manipulation and careful handling of multiple solutions, but follows a standard solution pathway once the substitution is made. |
| Spec | 1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=11.05k Further identities: sec^2=1+tan^2 and cosec^2=1+cot^21.05o Trigonometric equations: solve in given intervals |
Solve the equation
$$2\tan^2\theta + 2\tan\theta - \sec^2\theta = 2,$$
for values of $\theta$ between $0°$ and $360°$. [5]
\hfill \mbox{\textit{WJEC Unit 3 2018 Q4 [5]}}