June 2024 Paper 2 Q4

OCR MEICurrent spec5 marksRadians Trigonometry

(a) On the axes in the Printed Answer Booklet, sketch the graph of \(y = \sin 2\theta\) for \(0 \leqslant \theta \leqslant 2\pi\). [2]

(b) Solve the equation \(\sin 2\theta = -\dfrac{1}{2}\) for \(0 \leqslant \theta \leqslant 2\pi\). [3]

Sketch of y = sin 2θ for 0 to 2π: two complete sine cycles with amplitude 1, crossing the axis at π/2, π, 3π/2 and 2π — Mark scheme (a)

Scheme	Marks	AO
	M1 A1	1.1 1.1
	[2]

Mark scheme (b)

Scheme	Marks	AO
either \(-\frac{\pi}{12}\) or \(-\frac{5\pi}{12}\) oe seen or either \(\frac{7\pi}{6}\) or \(\frac{11\pi}{6}\) oe seen	M1	3.1a
\(\frac{7\pi}{12}, \frac{11\pi}{12}, \frac{19\pi}{12}, \frac{23\pi}{12}\)	A1 A1	1.1 1.1
	[3]

Notes

M1: NB from use of \(\sin^{-1}\left(-\frac{1}{2}\right)\)
NB \(-0.262\) or \(-1.309\); decimals correct to 2 dp or better
or
3.665 or 5.760; decimals correct to 2 dp or better
M1 may be implied by two correct answers in radians

A1: two correct values
NB awrt 1.833, 2.880, 4.974, 6.021 or correct to 2 dp

A1: all four values correct with no extras for \(0 \leqslant \theta \leqslant 2\pi\)
if M0A0A0 allow SCB1 for two correct answers in degrees or SCB2 for all four correct in degrees 105, 165, 285 and 345