Moderate -0.8 This is a straightforward application of solving sin(x) = k with a double angle, requiring students to find the principal value, identify the second solution in [0, 2π], then divide by 2 to get θ values. It's routine C2 material with no conceptual challenges beyond basic inverse trig and the double angle substitution.
8 Solve the equation \(\sin 2 \theta = 0.7\) for values of \(\theta\) between 0 and \(2 \pi\), giving your answers in radians correct to 3 significant figures.
A1 each value; if any final answers not given to 3 sf deduct 1 mark from total A marks
in degrees: \(22.2,\ 67.8,\ 202,\ 248\)*
if A0 then B1 for at least two of \(2.366\ldots,\ 7.058\ldots,\ 8.649\ldots\) for \(2\theta\) or all of \(135.57\ldots,\ 404.427\ldots,\ 495.57\ldots\); *if final answers in degrees deduct 1 from total A marks; ignore extra values outside range; if four correct answers in degrees or radians, deduct 1 for extra values in range
## Question 8:
| Answer | Marks | Guidance |
|--------|-------|----------|
| $0.775397\ldots$ soi | M1 | or $44.427\ldots°$ |
| $0.388,\ 1.18,\ 3.53,\ 4.32$ | A4 | A1 each value; if any final answers not given to 3 sf deduct 1 mark from total A marks |
| in degrees: $22.2,\ 67.8,\ 202,\ 248$* | | if A0 then B1 for at least two of $2.366\ldots,\ 7.058\ldots,\ 8.649\ldots$ for $2\theta$ or all of $135.57\ldots,\ 404.427\ldots,\ 495.57\ldots$; *if final answers in degrees deduct 1 from total A marks; ignore extra values outside range; if four correct answers in degrees or radians, deduct 1 for extra values in range |
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8 Solve the equation $\sin 2 \theta = 0.7$ for values of $\theta$ between 0 and $2 \pi$, giving your answers in radians correct to 3 significant figures.
\hfill \mbox{\textit{OCR MEI C2 2012 Q8 [5]}}