Thisactivity is about Analog clocks and also the angle made through thehands that the clock. Girlfriend can discover out more about angles and how they"re measure on thepage Degrees(Angles).

You are watching: What is the angular position in radians of the minute hand of a clock at 7:00?

What is the angle in between the hands of a clock at 1 o"clock?


at 1 o"clock the minute hand(red) points come the 12 and thehour hand (blue) points to the 1.So we need to find the angle betweenthe 12and the 1.

How plenty of of this angle are there in a finish turn?


There room 12 of lock in a complete turn (360°), so eachonemust be360°÷ 12= 30°

for this reason the angle betweenthehandsof a clock in ~ 1 o"clock is30°.


It doesn"tmatter even if it is we are talking about 1 to be or 1pm, the price is exactly the same for both.The angle in between the hands at1 o"clock could additionally be offered as the reflex edge 330°,but us willalways offer the smaller sized (acute or obtuse) angle.

What is the anglebetween the hand of a clock in ~ 2:30?


At 2:30 the minute hand(red) points come the 6 and also the hour hand(blue) points halfway between the 2 and also the 3.

for this reason how numerous lots that 30° carry out we have actually this time?


The angle in between the 5 and also the 6 is30°The angle between the 4 and the5 is30°The angle between the 3 and the4 is30°The staying angle is½ × 30° = 15°

therefore the anglebetween the hands of a clock at2:30 = 30° + 30° + 30° + 15° = 105°

Your Turn

finish the following table (give the smaller sized angle in every case):


Check her answers in ~ the bottom of the page.

More facility Times

Finding the angle in between the hand of a clock is easy as longas us don"t use complicated times.

For example finding the anglebetween the hand at 9:37 is much more difficult. You have the right to trythat one if girlfriend wish, however it"s most likely too hard.

Example: Atwhat time is the angle in between the hand of a clock same to30°?

notice that the inquiry asks for "times".There are numerous possibleanswers.Some of lock are basic to find, rather much much more difficult.

Here space two simple answers:

1 o"clock11 o"clock
But what aboutthis one?
4:15 PM

At very first glance, it looks favor this can be a 30° angle also,but at 4:15, the hour hand has currently moveda quarter of the means between the 4 and the 5.

So theangle is30°+ ¼ × 30° = 30° + 7½° = 37½°.

This might be a more accurate answer:


deserve to you find more 30° angles prefer this one?

At what times of the day perform the hand of a clock lie in a straightline?

In other words the angle between them is 180°?

One apparent answer is 6 o"clock:


But what other answers might there be?

9:15 is no correct because that a similar reason the 4:15 didn"t provide us precisely a30° edge ... The hour hand has moved on beyond the 9.

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This seems to it is in a very challenging question to answer, yet there is aneasy way.

How many times between 6:00 am and 6:00 pm execute the hands make astraight line?

There must be at the very least one allude time because that each hour:

one in between 7:00 am and 8:00 am, one in between 8:00 am and 9:00 am, one between9:00 am and 10:00 am, etc, up to between 4:00 pm and also 5:00 pm

That makes 11 equal parts, and so: