Let be a fixed angle

MATHEMATICS · Single correct · GCSE · Mathematics · Geometry and Measures · Geometry and Measures

Problem

Let 0<α<π20 < \alpha < \frac{\pi}{2} be a fixed angle. If P=(cos⁡θ,sin⁡θ)P = (\cos \theta, \sin \theta) and Q=(cos⁡(α−θ),sin⁡(α−θ))Q = (\cos(\alpha - \theta), \sin(\alpha - \theta)) , then Q is obtained from P by (1) clockwise rotation around origin through an angle α\alpha (2) anti-clockwise rotation around origin through an angle α\alpha (3) reflection in the line through origin with slope tan⁡α\tan \alpha (4) reflection in the line through origin with slope tan⁡(α2)\tan\left(\frac{\alpha}{2}\right)

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