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NDA 2014
Exam
NDA
Year
2014
Subject
Mathematics
Chapter
Trigonometric Ratios & Identities

NDA 2014 · Mathematics · Trigonometric Ratios & Identities

Consider the following statements: 1. If 3 θ is an acute angle such...

Consider the following statements: 1. If 3θ3 \theta is an acute angle such that sin⁡3θ=cos⁡2θ\sin 3 \theta=\cos 2 \theta, then the measurement of θ\theta in radian equals to π10\frac{\pi}{10}. 2. One radian is the angle subtended at the centre of a circle by an arc of the same circle whose length is equal to the diameter of that circle. Which of the above statements is/are correct?

Options

  1. A1 only
  2. B2 only
  3. CBoth 1 and 2
  4. DNeither 1 nor 2

Correct answer

A. 1 only

Step-by-step solution

sin⁡3θ=cos⁡2θ⇒cos⁡(90∘−3θ)=cos⁡2θ⇒90∘−3θ=2θ⇒5θ=90∘⇒θ=18∘∴180∘=π radian ∴18∘=π180×18=π10 radian \begin{aligned} & \sin 3 \theta=\cos 2 \theta \\ & \Rightarrow \cos \left(90^{{}^{\circ}}-3 \theta\right)=\cos 2 \theta \\ & \Rightarrow \quad 90^{{}^{\circ}}-3 \theta=2 \theta \\ & \Rightarrow \quad 5 \theta=90^{{}^{\circ}} \\ & \Rightarrow \quad \theta=18^{{}^{\circ}} \\ & \therefore \quad 180^{{}^{\circ}}=\pi \text{ radian } \\ & \therefore \quad 18^{{}^{\circ}}=\frac{\pi}{180} \times 18=\frac{\pi}{10}\text{ radian } \end{aligned}1 is true. 2 is not true.$
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