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NDA 2019 Maths · Mathematics · Trigonometric Functions and Identities · easy

If cot θ=5/12 and θ lies in the third quadrant, then sin θ equals

Single correct option

If cot⁡θ=512\cot\theta=\dfrac5{12} and θ\theta lies in the third quadrant, then sin⁡θ\sin\theta equals
  1. A. −1213-\dfrac{12}{13}
  2. B. 1213\dfrac{12}{13}
  3. C. −513-\dfrac{5}{13}
  4. D. −1312-\dfrac{13}{12}
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Answer: (A) −1213-\dfrac{12}{13}

From cot⁡θ=512\cot\theta=\dfrac5{12} the sides are 55 (adjacent), 1212 (opposite) and hypotenuse 1313. So ∣sin⁡θ∣=1213|\sin\theta|=\dfrac{12}{13}. In the third quadrant both sine and cosine are negative, therefore sin⁡θ=−1213\sin\theta=-\dfrac{12}{13}. The value −513-\dfrac5{13} is cos⁡θ\cos\theta and 1213\dfrac{12}{13} ignores the quadrant.
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Original question written in the NDA 2019 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake