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NDA 2013
Exam
NDA
Year
2013
Subject
Mathematics
Chapter
Trigonometric Ratios & Identities

NDA 2013 · Mathematics · Trigonometric Ratios & Identities

What is the angle (in circular measure) between the hour hand and...

What is the angle (in circular measure) between the hour hand and the minute hand of a clock when the time is half past 4?4 ?

Options

  1. Aπ3\frac{\pi}{3}
  2. Bπ4\frac{\pi}{4}
  3. Cπ6\frac{\pi}{6}
  4. DNone of the above

Correct answer

B. π4\frac{\pi}{4}

Step-by-step solution

Angle rotated by minute hand in 30 minutes =3060×360∘=180∘=\frac{30}{60} \times 360^{{}^{\circ}}=180^{{}^{\circ}} Angle rotated by hour hand when it is at 4.5 =4.512×360∘=135∘=\frac{4.5}{12} \times 360^{{}^{\circ}}=135^{{}^{\circ}} Angle between two hands =180∘−135∘=45∘=180^{{}^{\circ}}-135^{{}^{\circ}}=45^{{}^{\circ}}
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