How to find the angle between the hour hand and the minute hand, and how to calculate the angle betw

At 2:30, the angle between the hour and minute hands is 105 degrees.

180 is the angle at which the minute hand goes, 30 minutes * 360 degrees 60 minutes = 180 degrees;

60 is the angle at which the hour hand has traveled independently, 2 o'clock * 360 degrees 12 o'clock = 60 degrees;

The angle of the hour hand = the angle of the hour hand walking independently + the angle at which the minute hand drives the hour hand (180 * 1 12 = 30 minutes * 360 degrees 12 hours 60 minutes = 15 degrees).

The angle between the hour hand and the minute hand = the angle of the minute hand - the angle of the hour hand = 180 - (60 + 180 * 1 12) = 105 degrees.

Let the scale mark at 12 o'clock be 0 degrees, as the starting line of the angle, and the position of the two hands at any time x hour and y minutes, because the minute hand turns 360 60 6 degrees per minute, the hour hand turns 360 (12*60) degrees per minute, and the hour hand turns 360 12 30 degrees every 1 hour, so:

At x hour y, the angle between the hour hand and the starting line of 0 degrees ** over angle) is: 30x, at x hour y, the angle between the minute hand and the starting line of 0 degrees ** over angle) is: 6y, the calculation formula for the angle between the hour hand and the minute hand is:

6y-(30x+, in degrees (°).)

Traditionally, angles over 180° are generally used for angles smaller than 180° (360°-|Indicates the angle at which they are in.

The above process works at any time)!

For example, the angle between the two needles at 8:30: substituting x 8, y 30 into the above equation, the angle is 75°

Another example, the angle between the two needles at 12:55: substitute x 12, y 55 into the above equation to obtain the angle

For example, the angle between the two needles at 11:03: substitute x 11, y 3 into the above formula, and obtain the angle; The angle between the two pins at 360° at 11:03 is.

The method of calculating the open root number.

At 2:30, the minute hand is at the 6 position, and the 6 is at a 180-degree angle to the 12.

Scale 12 - scale 6 is 180 degrees angle, at 2 o'clock, the hour hand moves 1 3 * 180 = 60

So, 180-60

180x1 12 refers to, 30 minutes, the scale traveled by the hour hand. Because it is impossible for the hour hand to stop at 2:30 on the 2 scale. So to subtract.

The hour hand turns 360° in 12 hours, so the hour hand turns 30° every hour, that is, 60 minutes turns 30°, so every minute turns; The minute hand turns 360° in 1 hour, that is, 360° in 60 minutesThen the absolute value of the difference between the angle of the hour hand and the angle of the minute hand can be calculated in turn by 6° per minute; When this value is greater than 180 degrees, subtract the difference from 360 degrees.

In the equation, "180" means that the minute hand has been turned 180 degrees in 30 minutes, and the calculation process is 30*6=180;In the equation, "60" is the rotation of the hour hand for 2 hours; In the equation 180 1 12 is the angle at which the hand turns for 30 minutes, i.e. 15 degrees. In short, 180-60-180 1 12=105 degrees, in the question at 2:30, the angle angle of the hour hand and the minute hand is 105 degrees.

Vector analysis: In mathematics, the smallest positive angle formed by the intersection of two lines (or vectors) is called the angle between these two lines (or vectors), which is usually denoted as (included angle), and the interval range of the angles is .

Corners are usually represented by three letters: the letters of the dots on the two sides are written on both sides, and the letters on the vertices are written in the middle. The corners in the diagram are represented by AOB. However, in the absence of confusion, it is also represented directly by the letter of the vertex, such as the corner o.

It is common to use the Greek letter ( to indicate the size of the horn. To avoid confusion, symbols are generally not used to indicate angles.

The key to solving the problem of the angle between the hour hand and the minute hand is to engage in it.

The angle at which the hour and minute hands turn every minute on the clock face is the minute hand.

6° per minute (one small block on the clock face); The hour hand turns 30° per hour, and the hour hand turns 0 5° per minute Therefore, for m point n minutes: the degree of the hour hand is m 30° + n 0 5°, and the degree of the minute hand is n 6°, so the angle between the hour hand and the minute hand =|m×30°+n×0．5°-n×6°|, i.e. =|

m×30°-n×5．5°|If the angle obtained by the above equation is greater than 180°, the angle between the hour hand and the minute hand should be 360° minus the angle obtained by the above equation, i.e. 360°-

The key to solving the problem of the angle between the hour hand and the minute hand is to engage.

The angle at which the hour and minute hands turn every minute on the clock face is the minute hand.

6° per minute (one small block on the clock face); The hour hand turns 30° per hour, and the hour hand turns 0 5° per minute Therefore, for m point n minutes: the degree of the hour hand is m 30° + n 0 5°, and the degree of the minute hand is n 6°, so the angle between the hour hand and the minute hand =|m×30°+n×0．5°-n×6°|, i.e. =|

m×30°-n×5．5°|If the angle obtained by the above equation is greater than 180°, the angle between the hour hand and the minute hand should be 360° minus the angle obtained by the above equation, i.e. 360°-

Answer: Hello, the formula for calculating the degree of the angle between the hour hand and the minute hand: Let the scale mark at 12 o'clock be 0 degrees, as the starting line of the angle The position of the two hands at any time at x hour and y minutes Because the minute hand turns 360 60 6 degrees per minute The hour hand turns 360 (12*60) degrees per minute The hour hand turns 360 12 30 degrees at x hour and y minutes, the angle between the hour hand and the starting line of 0 degrees ** over the angle is: 30x At x hour y minutes, the angle between the minute hand and the starting line of 0 degrees ** over the angle) is:

6y pro information: the number of angles between the two hands on the hour hand = ( (m = minutes, h = hours) Note: The 12-hour chronograph system must be used, where it is full of 12:

00 hours must be subtracted by 12. Whether an object rotates clockwise or counterclockwise depends on the angle of view. For example, the rotation of the Earth is counterclockwise from directly above the North Pole**, and clockwise from directly above the South Pole.

The minute hand rotates at an angle of six degrees for every one small block on the clock, and every numeral movement takes five minutes and rotates at an angle of 30 degrees.

Analysis: 1. Calculate the angle in the clockwise direction: the angle from 12 o'clock to 7 o'clock is 210 degrees, and the angle from 12 o'clock to 8 is 240 degrees

2. For every minute hand walking, the angle formed by the minute hand is 360 60 = 6 degrees 3, and the minute hand goes for one hour for each circle, and the angle formed by the hour hand is 30 degrees. From this, it can be seen that for every minute hand that travels, the angle formed by the hour hand is 30 60 = degrees.

4. There are two possibilities for the angle between the minute hand and the hour hand.

Set Xiaohua to start writing homework at 7 o'clock x and finish homework at 8 o'clock y. The column equation is as follows:

Possibility one: 210+

x = 20 points.

Possibility two: 210+

x = point probability one: 240+

y = point probability two: 240+

y=60 points, which does not fit the topic.

That is, Xiaohua may start writing her homework at 7:20 or 7 o'clock. The time to finish the assignment is 8 o'clock. The time spent is: minutes or minutes.

When the time is m point n minutes, the degree of the angle between the hour hand and the minute hand is:

1) The minute hand is in front of the hour hand: that is, when n>=60 11m.

2) The minute hand is behind the hour hand: i.e. at N<60 11m.

1. Knowledge preparation.

1) Ordinary clocks and watches are equivalent to circles, and their hour or minute hands are equivalent to walking around a 360° angle;

2) The angle of each block on the clock (one hour of the hour hand or five minutes of the minute hand) is: <>

3) The angle corresponding to every 1 minute of the hour hand should be: <>

4) The angle of the minute hand should be <> for every 1 minute that passes

2. Calculation examples.

Analysis: According to common sense, we should start with the hour and minute hands at 12 o'clock. Since the minute hand is in front of the hour hand, we can first calculate the angle at which the minute hand has traveled, and then subtract the angle at which the hour hand has traveled, and then we can find the degree of the angle between the hour hand and the minute hand.

The angle at which the minute hand travels is: 55 6° 330°

The angle at which the hour hand travels is:

Then the degree of the angle between the hour hand and the minute hand is:

<> analysis: In this problem, the minute hand is behind the hour hand, which is different from the previous question, we should first calculate the angle of the hour hand, and then subtract the angle of the minute hand to find the degree of the angle between the hour hand and the minute hand.

The angle at which the hour hand travels is:

The angle at which the minute hand travels is:

Then the degree of the angle between the hour hand and the minute hand is:

3. Summarize the rules.

From the above two examples, we can summarize the following rules: when the minute hand is in front of the hour hand, we can first calculate the angle of the minute hand, and then subtract the angle of the hour hand to find the degree of the angle between the hour hand and the minute hand; When the minute hand is behind the hour hand, you can calculate the angle of the hour hand first, and then subtract the angle of the minute hand to find the degree of the angle between the hour hand and the minute hand.

Represented by letters and formulas:

When the time is m point n minutes, the degree of the angle between the hour hand and the minute hand is:

1) The minute hand is in front of the hour hand:

2) The minute hand is behind the hour hand:

According to this formula, you can find the degree of the angle between the hour hand and the minute hand at any time, which is very easy to calculate. If seconds are involved in the question, we can convert seconds to minutes first, and then apply the above rules and formulas to calculate.

The number of angles between the hour and minute hands at any given moment is equal to the absolute value of the difference between the hours and minutes and the number of 30°-minutes.

Let the time grinding be x hours y minutes, with 12:00 as the 0 degree reference, and the angle of the minute hand is y 60 * 360 degrees = 6y degrees; In addition to considering x, the hour hand should also consider y, and the angle should be x 12 * 360 degrees + y 60 * 1 12 * 360 degrees = (30x + degrees, so the angle is the difference between the two = 6y-(30x+ degrees = (degrees.) For example: at 2:25, the angle is (degree = degree After the most guerrilla attack, it is also necessary to consider the situation of paying the value, and when there is a negative value uproar, 360 degrees must be added (the angle is less than 180 degrees).

For example: at 10:20, the angle is (degrees, plus 360 degrees = 170 degrees.

What is the formula for the angle between the hour and minute hands?

The hour hand travels half a degree per minute, and the minute hand travels six degrees per minute.

Calculate the angle between the hour hand and the minute hand, calculate it by the following method, and then take the absolute value, multiply the number of hours by 30 °, subtract the number of minutes, and multiply if the difference is greater than 180 °, and then subtract from 360 °.

The angle between the position of the hour hand and the hour point is the minute hand divided by sixty times thirty degrees (of each hour); The minute hand is six degrees (per minute) multiplied by the number of minutes. The two pins are reduced to the included angle.

There is no formula. Just remember that one large cell is 30° and a small cell is 6°.

The formula for calculating the degree of the hour hand and the minute hand is carefully burned to imitate the angle: Let the scale mark of silver in 12 periods be 0 degrees, as the angle from the width of the fiber point line The position of the two hands at any time x hour y minute Because the minute hand turns 360 per minute 60 = 6 degrees The hour hand turns 360 per minute (12 * 60) = degrees The hour hand turns every 1 hour.

In fact, it is a simple trigonometric formula, the formula of tan.

The formula for calculating the angle between the hour and minute hands is the duel value of s = ( (n = n hours m = m minutes s = s degrees).

The formula for calculating the degree of the angle between the hour and minute hands:

Let the tick mark at 12 o'clock hit the core at 0 degrees, as the starting line of the angle.

The position of the two hands at any time x hour and y minutes.

Because the minute hand turns 360 beats per minute, 60 6 degrees.

The hour hand is 360 (12*60) degrees per minute.

The hour hand turns 1 degree 360 12 every 30 hours.

At x hour y, the angle between the hour hand and the starting line of 0 degrees ** over the angle) is: 30x at x hour y, the angle between the minute hand and the starting line of 0 degrees ** over angle) is: 6y

When the minute hand is in front of the hour hand, the clamp angle is formulated as n*6°-(m*30°+n*, when the minute hand is behind the hour hand, the clamp angle is (m*30°+n*). where n is the minute and m is the hour.

A degree is a number obtained by measuring in degrees, and refers to the standard used for measurement. A clock is a precision instrument that measures and indicates time. In mathematics, the smallest positive angle formed by the intersection of two straight lines is called the angle between these two straight lines (or vectors).

A common form of clock problem is clock face chasing. The problem of clock face tracking is usually a problem that studies the position between the hour and minute hands, such as "the coincidence of the minute and hour hands, perpendicular, straight lines, and how many degrees of angle are formed". The hour and minute hands move in the same direction, but at different speeds, similar to the catch-up problem in the travel problem.

The key to solving such problems is to determine the speed or speed difference of the hour and minute hands.

In the specific process of solving the problem, we can use the grid method, when the circumference of the clock face is evenly divided into 60 cells, each grid is called 1 grid. The minute hand travels once an hour, i.e. 60 minutes, while the hour hand travels only 5 minutes per hour, so the minute hand travels 1 minute per minute, and the hour hand travels 1 12 minutes per minute. The speed difference is 11 to 12 divisions.

It is also possible to use the degree method, that is, from an angle point of view, the circumference of the clock face is 360 °, and the minute hand rotates 360 60 degrees per minute to rise the virtual code, that is, the speed of the minute hand is 6 ° min, and the hour hand turns 360 12 = 30 degrees per hour, so the speed per minute is 30 ° 60, that is. The difference in speed between the minute hand and the hour hand is.