Stepwise
Start practisingPractise

WAEC 2023 · Paper 1 · Q40

Given that sin⁡x=45\sin x = \frac{4}{5} and cos⁡y=1213\cos y = \frac{12}{13}, where xx is an obtuse angle and yy is an acute angle, find the value of sin⁡(x−y)\sin(x - y).

Worked solution (try it first)
  1. xx is obtuse, so its cosine is negative: cos⁡x=−35\cos x = -\frac{3}{5}.
  2. yy is acute, so sin⁡y=513\sin y = \frac{5}{13}.
  3. Use sin⁡(x−y)=sin⁡xcos⁡y−cos⁡xsin⁡y\sin(x - y) = \sin x\cos y - \cos x\sin y.
  4. Put in the values: 45⋅1213−(−35)513=4865+1565\frac{4}{5} \cdot \frac{12}{13} - \left(-\frac{3}{5}\right)\frac{5}{13} = \frac{48}{65} + \frac{15}{65}.
  5. So sin⁡(x−y)=6365\sin(x - y) = \frac{63}{65}, option D.

Report a problem with this question