Consider the analogue clock below, which has a circular face with centre at point O. The minute hand of the clock, OP, has a length of 12 cm and the hour hand, OQ, has a length of 10 cm.
In Figure: 1 the time on the clock is 7:00 pm.
1.For Figure: 1, find
(1)the size of the reflex angle, $P\widehat{O}Q$, in degrees. $^{\circ}$
(2)the distance between the ends of the hour and minute hands.
In Figure: 2, the time is now 7:18 pm, and as such, the end point of the minute hand has rotated through an angle, θ, covering an arc length of l . ≈ cm
2.For figure: 2, find
(1)the size of the angle θ in degrees. $^{\circ}$
(2)the arc length l. ≈ cm
(3)the area of the shaded sector. ≈ $cm^2$
Another circular analogue clock, show n below, has a face radius of 14 cm, and minute and hour hands of length 14 cm14 cm. The current time shown on the clock is 6:00 pm. The bottom of the clock face is 4cm above the base of the frame holding the clock.
The height, h, of the end point of the minute hand above the base of the frame is modelled by the function
h(θ)=14cosθ+18
where θ is the angle rotated by the minute hand after 6:00 pm.
3.Find the value of h when θ=$170^{\circ}$
The height, g, of the end point of the hour hand above the base of the frame is modelled by the function
g(θ)=−14cos($\frac{θ}{12})$+18
where θ is the angle rotated by the minute hand after 6:00 pm.
The end points of the minute and hour hands have the same height from the base of the frame for the first time when θ=k. ≈ cm
