The key is to find out the angle at which the hour hand and the minute hand rotate every minute on the clock face. The minute hand turns 6 degrees per minute (a small square on the clock face); The hour hand turns 30 every hour, and the hour hand turns 0.5 every minute. Therefore, for m points and n minutes, when the hour hand rotates m× 30+n× 0.5 and the minute hand rotates n× 6, the included angle between the hour hand and the minute hand is α = | m× 30+n× 0.5-n× 6 |. Then the angle between the hour hand and the minute hand should be 360 MINUS the angle obtained from the above formula, that is, 360-α. The key to solve the angle problem between the hour hand and the minute hand is to find out the angle at which the hour hand and the minute hand rotate every minute. The minute hand turns 6 per minute (the small square on the dial). The hour hand turns 30 per hour and the hour hand turns 0.5 per minute. Therefore, for m points and n minutes, the degree of rotation of the hour hand is m× 30+n× 0.5, and the degree of rotation of the minute hand is n× 6, so the included angle between the hour hand and the minute hand is included.

α = | m× 30+n× 0.5-n× 6 |, which means α = | m× 30-n× 5.5 |. If the angle obtained by the above formula is greater than 180, the angle between the hour hand and the minute hand should be 360 minus the angle obtained by the above formula, that is, 360.

How to calculate the angle between the hour hand and the minute hand

In junior high school mathematics teaching, clock problems often appear, and it is difficult for students to calculate, especially in calculating the angle between the hour hand and the minute hand, which has been puzzling many teachers' teaching because of its many calculation methods. Based on my own teaching experience, this paper summarizes the rules and methods that make this kind of calculation more convenient for your reference.

First, knowledge preparation

(1) An ordinary clock is equivalent to a circle, and its hour hand or minute hand is equivalent to walking 360 degrees;

(2) The angle corresponding to each grid on the clock (hour hand 1 hour or minute hand 5 minutes) = 30;

(3) The angle of the hour hand every 1 min should be: = 0.5;

(4) The minute hand angle per 1 min should be = 6.

Second, the calculation example

Example 1: As shown in figure 1, when the time is 7: 55, calculate the angle between the hour hand and the minute hand (excluding the angle greater than 180).

Analysis: According to common sense, it should start from the hour hand and the minute hand 12. Since the minute hand is in front of the hour hand, we can first calculate the angle that the minute hand passes through, and then subtract the angle that the hour hand passes through, and then we can work out the degree of the included angle between the hour hand and the minute hand.

The minute hand passes through the following angles:

55×6 =330 .

The angle through which the hour hand passes is:

7×30 +55×0.5 =237.5 .

When the time is x, the minute is y, starting from 12: 00, and the minute hand angle is y/60 * 360 = 6y; In addition to X, clockwise hand should also consider Y. The angle should be x/ 12*360 degrees+Y/60 *112 * 360 degrees =(30x+0.5y) degrees, so the included angle is the difference between them = 6y-(30x Example: 2: 25, the included angle is (5.5*25-30*2) degrees =77.5 degrees.

Finally, we should consider the payment value. When there is a negative value, you must add 360 degrees (the included angle is less than 180 degrees).

Example: At 10: 20, the included angle is (5.5 * 20-30 *10) =-190 degrees, plus 360 degrees = 170 degrees.