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Q.
Find in radians, the angle between the hour hand and the minute hand of a clock at half past three.
Trigonometric Functions
Solution:
The angle traced by the hour hand in $12$ hrs $= 360^{\circ}$
$\therefore $ The angle traced by the hour hand in $3$ hrs $30$ mins
i.e., $\frac{7}{2}hr=\left(\frac{360}{12}\times\frac{7}{2}\right)^{\circ}=105^{\circ}$
The angle traced by the minute hand in $60$ mins $= 360^{\circ}$
$\therefore $ The angle traced by the minute hand in $30$ mins
$=\left(\frac{360}{60} \times30\right)^{\circ}=180^{\circ}$
Hence, the required angle between two hands
$=180^{\circ}-105^{\circ}=75^{\circ}$
Required angle in radians $=\left(75 \times \frac{\pi}{180}\right)=\frac{5\pi}{12}rad$