Without using a calculator

MATHEMATICS · Subjective · A Level · Mathematics · Trigonometry · Trigonometry

Problem

Without using a calculator, compare the two numbers sin⁡(1007π6)\sin\left(\dfrac{1007\pi}{6}\right) and sin⁡(−113π12)\sin\left(-\dfrac{113\pi}{12}\right). (a) Reduce each angle to its principal value lying between −π-\pi and π\pi. (b) Hence obtain the exact value of each sine. (c) State which of the two values is greater and justify your answer. (d) Find the numerical value of sin⁡(1007π6)−sin⁡(−113π12)\sin\left(\dfrac{1007\pi}{6}\right)-\sin\left(-\dfrac{113\pi}{12}\right).

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