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NDA 2022
Exam
NDA
Year
2022
Subject
Mathematics
Chapter
Trigonometric Ratios & Identities

NDA 2022 · Mathematics · Trigonometric Ratios & Identities

If θ=-(5)/(12) , then what can be the value of θ ?

If tan⁡θ=−512\tan \theta=-\frac{5}{12}, then what can be the value of sin⁡θ\sin \theta ?

Options

  1. A513\frac{5}{13} but cannot be −513-\frac{5}{13}
  2. B−513-\frac{5}{13} but cannot be 513\frac{5}{13}
  3. C513\frac{5}{13} or −513-\frac{5}{13}
  4. DNone of the above

Correct answer

C. 513\frac{5}{13} or −513-\frac{5}{13}

Step-by-step solution

tan⁡θ=−512=pb;\tan \theta=\frac{-5}{12}=\frac{p}{b} ; Let p=5kb=12k∴h=p2+b2=25k2+144k2=13kp=5 k \quad b=12 k\therefore \quad \mathrm{h}=\sqrt{p^2+b^2}=\sqrt{25 k^2+144 k^2}=13 k Since value of tan⁡θ\tan \theta is - ve therefore θ\theta lies in 2 nd and 3rd quadrant. ∴sin⁡θ=ph=±513\therefore \quad \sin \theta=\frac{p}{h}= \pm \frac{5}{13}
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