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Trigonometric Functions · Class 11 · CBSE · Science Mathematics

If tan theta=-frac{5}{12} and theta lies in the fourth quadrant, then sin theta is:

Practice question from Trigonometric Functions (Class 11 · CBSE · Science Mathematics), with the correct answer and a step-by-step solution.

easy · MCQ · Q-9DE53D

If tan⁡θ=−512\tan \theta=-\frac{5}{12} and θ\theta lies in the fourth quadrant, then sin⁡θ\sin \theta is:

  1. A.513\frac{5}{13}
  2. B.−513-\frac{5}{13}Correct answer
  3. C.1213\frac{12}{13}
  4. D.−1213-\frac{12}{13}

Solution

Using a 55-1212-1313 triangle, ∣sin⁡θ∣=513|\sin\theta|=\frac{5}{13}. Since θ\theta is in the fourth quadrant, sine is negative; hence sin⁡θ=−513\sin\theta=-\frac{5}{13}.

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