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NDA 2024 Maths · Mathematics · Trigonometric Functions and Identities · easy

The angle θ is in the fourth quadrant with cos θ=8/17. The value of cosecθ is

Single correct option

The angle θ\theta is in the fourth quadrant with cos⁡θ=817\cos\theta=\dfrac8{17}. The value of cosec⁡θ\operatorname{cosec}\theta is
  1. A. 1715\dfrac{17}{15}
  2. B. −1517-\dfrac{15}{17}
  3. C. 178\dfrac{17}{8}
  4. D. −1715-\dfrac{17}{15}
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Answer: (D) −1715-\dfrac{17}{15}

sin⁡θ=−1−64289=−1517\sin\theta=-\sqrt{1-\frac{64}{289}}=-\frac{15}{17} (sine is negative in the fourth quadrant), so cosec⁡θ=−1715\operatorname{cosec}\theta=-\frac{17}{15}. Trap: dropping the sign, or quoting sin⁡θ\sin\theta instead of its reciprocal.
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