Edexcel C2 — Question 3 6 marks

Exam BoardEdexcel
ModuleC2 (Core Mathematics 2)
Marks6
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TopicQuadratic trigonometric equations
TypeSolve equation given in radians/exact form
DifficultyModerate -0.8 This is a straightforward quadratic in tan²θ requiring only rearrangement to tan²θ = 1/3, taking square roots to get tanθ = ±1/√3, and recognizing these as standard angles (π/6). The interval and symmetry make finding all four solutions routine. Below average difficulty for C2.
Spec1.05o Trigonometric equations: solve in given intervals
3. Giving your answers in terms of \(\pi\), solve the equation $$3 \tan ^ { 2 } \theta - 1 = 0 ,$$ for \(\theta\) in the interval \(- \pi \leq \theta \leq \pi\).
AnswerMarks Guidance
\(\tan^2 \theta = \frac{1}{3}\)M1
\(\tan \theta = \pm\frac{1}{\sqrt{3}}\)A1
\(\theta = \frac{\pi}{6}, \frac{5}{6} - \pi \text{ or } \pi - \frac{\pi}{6}, \frac{\pi}{6}\)B1 M1
\(\theta = -\frac{5\pi}{6}, -\frac{\pi}{6}, \frac{\pi}{6}, \frac{5\pi}{6}\)A2 (6) 
$\tan^2 \theta = \frac{1}{3}$ | M1 |

$\tan \theta = \pm\frac{1}{\sqrt{3}}$ | A1 |

$\theta = \frac{\pi}{6}, \frac{5}{6} - \pi \text{ or } \pi - \frac{\pi}{6}, \frac{\pi}{6}$ | B1 M1 |

$\theta = -\frac{5\pi}{6}, -\frac{\pi}{6}, \frac{\pi}{6}, \frac{5\pi}{6}$ | A2 | (6)
3. Giving your answers in terms of $\pi$, solve the equation

$$3 \tan ^ { 2 } \theta - 1 = 0 ,$$

for $\theta$ in the interval $- \pi \leq \theta \leq \pi$.\\

\hfill \mbox{\textit{Edexcel C2  Q3 [6]}}
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