If θ is an angle one measured in radian and θ∈ [0, 2 π ] then r θ is length of arc AB, of circle of radius r, subtending angle θ at the centre O, of the circle. Area of sector OAB is 
r 2 θ
(i) The angle between minute hand and hour hand of a clock at "half past 4" equals -
Text Solution
Verified by ExpertsA
(i)
Angle subtended by two consecutive marks at centre
=30º
Hence at "half past 4" the angle is 45º
(ii)
Distance covered in 1second = 5 
= 5 π cm.
Distance covered in 1 hr. = 
× 60 × 60
= 56.52 
57 km/hr.
(iii)
Area of region ABC = 
Area of OAB = 
r 2 .2 θ = r 2 θ
Area of Δ OAC = 
r 2 sin θ = Area of Δ OBC
∴ 
r 2 sin θ + 
r 2 sin θ + r 2 θ = 
⇒ 3sin θ + 3 θ = π
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