Moderate -0.5 This is a straightforward multiple angle equation requiring only the definition of cotangent, taking the inverse, and dividing by 2 to find θ. The main challenge is remembering to find all solutions in the extended range for 2θ (0° to 720°), but this is a standard technique taught early in C4 with minimal problem-solving required.
\(\Rightarrow 2\theta = 11.30...\) or \(180 + 11.30...\) or ...
B1
\(\Rightarrow \theta = 5.654...\) or \(90 + 5.654...\) or ...
\(= 5.7\) or \(95.7\) or \(185.7\) or \(275.7\) to 1dp, within the given range
B2
B2 for all four answers; B1 for only two
Total: 4
## Question 1:
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\tan 2\theta = 0.2$ | B1 | |
| $\Rightarrow 2\theta = 11.30...$ or $180 + 11.30...$ or ... | B1 | |
| $\Rightarrow \theta = 5.654...$ or $90 + 5.654...$ or ... | | |
| $= 5.7$ or $95.7$ or $185.7$ or $275.7$ to 1dp, within the given range | B2 | B2 for all four answers; B1 for only two |
| **Total: 4** | | |
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1 Solve the equation for values of $\theta$ in the range $0 ^ { \circ } < \theta < 360 ^ { \circ }$.
$$\cot 2 \theta = 5$$
\hfill \mbox{\textit{OCR MEI C4 Q1 [4]}}