Edexcel C2 — Question 3 6 marks

Exam BoardEdexcel
ModuleC2 (Core Mathematics 2)
Marks6
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicTrigonometric equations in context
TypeConvert sin/cos ratio to tan
DifficultyModerate -0.8 Part (a) is a straightforward algebraic manipulation to show tan θ = 2.5 by dividing through by cos θ. Part (b) applies the same result to 2x with a restricted domain, requiring only basic angle substitution and halving. This is simpler than average A-level questions as it involves minimal problem-solving—just direct application of trigonometric identities and calculator work.
Spec1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=11.05o Trigonometric equations: solve in given intervals
3. (a) Given that $$5 \cos \theta - 2 \sin \theta = 0 ,$$ show that \(\tan \theta = 2.5\) (b) Solve, for \(0 \leq x \leq 180\), the equation $$5 \cos 2 x ^ { \circ } - 2 \sin 2 x ^ { \circ } = 0 ,$$ giving your answers to 1 decimal place.
AnswerMarks Guidance
(a) \(5 \cos \theta = 2 \sin \theta\)M1
\(\frac{5}{2} = \frac{\sin \theta}{\cos \theta}\)
\(\tan \theta = 2.5\)A1
(b) \(\tan 2x = 2.5\)
\(2x = 68.199, 180 + 68.199\)B1 M1
\(2x = 68.199, 248.199\)
\(x = 34.1, 124.1\) (1dp)M1 A1 (6 marks) 
**(a)** $5 \cos \theta = 2 \sin \theta$ | M1 |
$\frac{5}{2} = \frac{\sin \theta}{\cos \theta}$ | |
$\tan \theta = 2.5$ | A1 |

**(b)** $\tan 2x = 2.5$ | |
$2x = 68.199, 180 + 68.199$ | B1 M1 |
$2x = 68.199, 248.199$ | |
$x = 34.1, 124.1$ (1dp) | M1 A1 | (6 marks)
3. (a) Given that

$$5 \cos \theta - 2 \sin \theta = 0 ,$$

show that $\tan \theta = 2.5$\\
(b) Solve, for $0 \leq x \leq 180$, the equation

$$5 \cos 2 x ^ { \circ } - 2 \sin 2 x ^ { \circ } = 0 ,$$

giving your answers to 1 decimal place.\\

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