2023 YTSS P1 Q9

2023 YTSS P1 Q9

Secondary 4
6 marks
  1. Express, in terms of \(\pi\), the principal value of
    1. \(\sin^{-1}\left(-\dfrac12\right)\),[1]
    2. \(\cos^{-1}\left(-\dfrac1{\sqrt2}\right)\).[1]
  2. State the set of values of \(x\) for which \(\cos^{-1}\left(-\dfrac12x\right)\) is defined.[1]
  3. Solve \(\sin(45^\circ-2x)=0.75\) for \(0^\circ\le x\le180^\circ\).[3]

Solution:

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Answer:(a)(i) \(-\dfrac\pi6\), (ii) \(\dfrac{3\pi}4\). (b) \(-2\le x\le2\). (c) \(136.8^\circ,178.2^\circ\).

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