Moderate -0.3 This is a straightforward application of solving sin(x) = k with a double angle, requiring students to find arcsin(0.7), identify the two solutions in [0, 2π] for 2θ, then divide by 2 to get four solutions for θ. It's slightly easier than average because it's a standard procedure with clear steps, though the double angle and finding all solutions adds minor complexity beyond basic recall.
5 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 A0 then B1 for at least two of 2.366..., 7.058..., 8.649... for \(2\theta\) or all of 135.57..., 404.427..., 495.57...
in degrees: 22.2, 67.8, 202, 248*
if any of final answers not given to three sf deduct 1 mark from total A marks; *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 5:
| Answer/Working | Mark | Guidance |
|---|---|---|
| 0.775397.. soi | M1 | or $44.427..°$ |
| 0.388, 1.18, 3.53, 4.32 | A4 | A1 each value; if A0 then B1 for at least two of 2.366..., 7.058..., 8.649... for $2\theta$ or all of 135.57..., 404.427..., 495.57... |
| in degrees: 22.2, 67.8, 202, 248* | | if any of final answers not given to three sf deduct 1 mark from total A marks; *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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5 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 Q5 [5]}}