UPSC CDS Math Trigonometric Ratios and Trigonometric Identities Questions

4:36 p.m. = 4 hours 36 minutes
=4+

36

60

=

23

5

hours
Angle traced by the hour hand in 12 hours =2π
Angle traced by the hour hand in

23

5

hours=

2π

12

×

23

5

=

23π

30

Angle traced by the minute hand in 60 minutes =2π
Angle traced by the minute hand in 36 minutes=

2π

60

×36=

36π

30

Therefore, angle between the hour hand and the minute hand of the clock when the time is 4:36 p.m.=θ
=

36π

30

−

23π

30

=

13π

30

Now,

12π

30

<

13π

30

<

18π

30

∴

2π

5

<θ<

3π

5