2017 · Q51
If θ measured in radians is the angle between the hour hand and the minute hand of a clock when the time is 4 : 36 pm, then which one of the following is correct ?
Elementary MathematicsTrigonometry
- A3π/5 < θ < 4π/5
- B2π/5 < θ < 3π/5
- Cπ/5≤θ≤2π/5
- D7π/15≤θ≤8π/15
Explanation
At 4:36 the minute hand is at 36×6° = 216° and the hour hand at 4×30°+36×0.5° = 138°, so the included angle is 78° = 13π/30 ≈ 0.433π. This lies between 2π/5 = 0.4π and 3π/5 = 0.6π. Hence option (B).