OCR MEI C2 (Core Mathematics 2)

1. Starting with an equilateral triangle, prove that \(\cos 30° = \frac{\sqrt{3}}{2}\). [2]
2. Solve the equation \(2 \sin \theta = -1\) for \(0 \leqslant \theta \leqslant 2\pi\), giving your answers in terms of \(\pi\). [3]

Use an isosceles right-angled triangle to show that \(\cos 45° = \frac{1}{\sqrt{2}}\). [2]

1. On the same axes, sketch the graphs of \(y = \cos x\) and \(y = \cos 2x\) for values of \(x\) from \(0\) to \(2\pi\). [3]
2. Describe the transformation which maps the graph of \(y = \cos x\) onto the graph of \(y = 3 \cos x\). [2]

\(\theta\) is an acute angle and \(\sin \theta = \frac{1}{4}\). Find the exact value of \(\tan \theta\). [3]

1. Sketch the graph of \(y = \cos x\) for \(0° \leqslant x \leqslant 360°\). On the same axes, sketch the graph of \(y = \cos 2x\) for \(0° \leqslant x \leqslant 360°\). Label each graph clearly. [3]
2. Solve the equation \(\cos 2x = 0.5\) for \(0° \leqslant x \leqslant 360°\). [2]

1. Sketch the graph of \(y = \sin \theta\) for \(0 \leqslant \theta \leqslant 2\pi\). [2]
2. Solve the equation \(2 \sin \theta = -1\) for \(0 \leqslant \theta \leqslant 2\pi\). Give your answers in the form \(k\pi\). [3]

Sketch the curve \(y = \sin x\) for \(0° \leqslant x \leqslant 360°\). Solve the equation \(\sin x = -0.68\) for \(0° \leqslant x \leqslant 360°\). [4]

1. Sketch the graph of \(y = \tan x\) for \(0° \leqslant x \leqslant 360°\). [2]
2. Solve the equation \(4 \sin x = 3 \cos x\) for \(0° \leqslant x \leqslant 360°\). [3]

Sketch the graph of \(y = \sin x\) for \(0° \leqslant x \leqslant 360°\). Solve the equation \(\sin x = -0.2\) for \(0° \leqslant x \leqslant 360°\). [4]