Mathematics

Problem

Without using a calculator, compare the two numbers

\sin\left(\dfrac{1007\pi}{6}\right)

and

\sin\left(-\dfrac{113\pi}{12}\right)

. (a) Reduce each angle to its principal value lying between

-\pi

and

\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\left(\dfrac{1007\pi}{6}\right)-\sin\left(-\dfrac{113\pi}{12}\right)

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