Clock formula for angle

I was given this interview question recently: Given a 12-hour analog clock, compute in degree the smaller angle between the hour and minute hands. Be as precise as you can. I'm wondering what's the simplest, most readable, most precise algorithm is. Solution in any language is welcome (but do explain it a bit if you think it's necessary). It turns out that Wikipedia does have the best answer: // h = 1..12, m = 0..59 static double angle(int h, int m) Basically: • The hour hand moves at the rate of 0.5 degrees per minute • The minute hand moves at the rate of of 6 degrees per minute Problem solved. And precision isn't a concern because the fractional part is either .0 or .5, and in the range of 0..360, all of these values are exactly representable in double. The java code that polygenlubricants is similar than mine. Let's assume that the clock is 12 hour instead of 24. If it's 24 hours, then that's a different story. Also, another assumption, assume if the clock is stopped while we calculate this. One clock cycle is 360 degree. • How many degree can the minute hand run per minute? 360 / 60 = 6 degree per minute. • How many degree can the hour hand run per hour? 360/12 = 30 degree per hour (since hour hand run slower than minute) Since it's easier to calculate in the unit, "minute", let's get "how many degree can the hour hand run per minute"? 30 / 60 = 0.5 degree per minute. So, if you know how to get those numbers, the problem is pretty much solved with this partial mathem...

$\begingroup$ I did some playing around on my calculator and found that if I make theta negative in the formula, it will give me the 2nd time the angle is formed, and according to the source of this problem, the answer would be correct, however it wouldn't be if I change the hour to 12 o'clock. $\endgroup$ Full circle is 60 minutes and $360^\circ$ so $$ 54^\circ = 54^\circ \times \frac = 9, $$ can you solve the equation? For a question of this type, "first time after $t_0$," there is a relatively straightforward procedure. Just ask and answer the following questions: • What is the angle between the hands at time $t_0$? • How much must the angle change to get to the desired angle? • How fast is the angle changing? (This one always has the same answer as long as the clock is a conventional 12-hour clock with minute and hour hands.) From the answers to questions 2 and 3, you figure out how long it takes for the hands to reach the desired configuration, and add that to $t_0$ to get the time when the configuration occurs. Just be careful that you correctly account for whether the minute hand has to catch up to the hour hand first and then get "ahead" by the given angle, or whether the minute hand can make that angle with the hour hand before catching up with it. Let's think it out. The minute hand travels $360 degrees/hour = 6 degrees/minute$. The hour hand travels $360 degrees/12 hour = 30 degrees/hour = .5 degree/minute$ So the angle between the two hands is $5.5 degrees*minu...

Activity: Clocks and Angles This activity is about What is the angle between the hands of a clock at 1 o'clock? At 1 o'clock the minute hand (red) points to the 12 and the hour hand (blue) points to the 1. So we need to find the angle between the 12 and the 1. How many of this angle are there in a complete turn? There are 12 of them in a complete turn (360°), so each one must be 360°÷ 12 = 30° So the angle between the hands of a clock at 1 o'clock is 30° . Note: • It doesn't matter whether we are talking about 1 am or 1 pm, the answer is exactly the same for both. • The angle between the hands at 1 o'clock could also be given as the reflex angle 330°, but we will always give the smaller (acute or obtuse) angle. What is the angle between the hands of a clock at 2:30? At 2:30 the minute hand (red) points to the 6 and the hour hand (blue) points halfway between the 2 and the 3. So how many lots of 30° do we have this time? • The angle between the 5 and the 6 is 30° • The angle between the 4 and the 5 is 30° • The angle between the 3 and the 4 is 30° • The remaining angle is ½× 30° = 15° So the angle between the hands of a clock at 2:30 = 30° + 30° + 30° + 15° = 105° Your Turn Complete the following table (give the smaller angle in each case): Time 1:00 2:30 7:00 10:30 11:20 3:40 5:15 8:45 Angle 30° 105° Check your answers at the bottom of the page. More Complicated Times Finding the angle between the hands of a clock is easy as long as we don't use complicated times. For exam...

Scope Pipe inspection, specifically Depending on the ILI tool type and vendor, the circumferential location of a call may be given in a clock position or degrees (typically measured “clockwise”, looking at the direction of flow, unless otherwise specified) and may need to be converted. This article will explain the basis for conversion between clock, degrees, and physical measurement, and how Microsoft Excel® quantifies clock as a value, which is then used to formulate the desired conversions. What is Clock? Clock is a unit of measurement on a circle, which is evenly divided into 12 units, with each unit equaling a value of one hour. Each hour is evenly divided into 60 sub-units, with each sub-unit equaling one minute. For the discussed purpose here, a given value in clock will be equivalent to a time value on a 12-hour clock. For a quick understanding of this, note that if you look at a clock face, 6:00 is at the bottom extent of the circle, 12:00 the top, 3:00 the right, and 9:00 the left. Twelve hours of 60 min each means there are 720 min in the 12-hour clock. This will be important to remember. What are Degrees? When given in degrees, a location on a circle is represented by 360 evenly divided units, usually measured from top dead center (0 in., or 12:00), or a designated reference point. In some cases, whole value degrees are sufficient. However, if a sub-unit is required, it can be designated as a decimal place value in tenths or hundredths. If exact conversions are...

Clock angle problems are a type of Math problem [ ] Clock angle problems relate two different measurements: A method to solve such problems is to consider the rate of change of the angle in degrees per minute. The hour hand of a normal 12-hour analogue clock turns 360° in 12 hours (720 minutes) or 0.5° per minute. The minute hand rotates through 360° in 60 minutes or 6° per minute. Equation for the angle of the hour hand [ ] θ hr = 0.5 ∘ × M Σ = 0.5 ∘ × ( 60 × H + M ) When are the hour and minute hands of a clock superimposed? [ ] T denotes time in hours; P, hands' positions; and θ, hands' angles in degrees. The red (thick solid) line denotes the hour hand; the blue (thin solid) lines denote the minute hand. Their intersections (red squares) are when they align. Additionally, orange circles (dash-dot line) are when hands are in opposition, and pink triangles (dashed line) are when they are perpendicular. In The hour and minute hands are superimposed only when their angle is the same. θ min = θ hr ⇒ 6 ∘ × M = 0.5 ∘ × ( 60 × H + M ) ⇒ 12 × M = 60 × H + M ⇒ 11 × M = 60 × H ⇒ M = 60 11 × H ⇒ M = 5. 45 ¯ × H H is an integer in the range 0–11. This gives times of: 0:00, 1:05. 45, 2:10. 90, 3:16. 36, 4:21. 81, 5:27. 27. 6:32. 72, 7:38. 18, 8:43. 63, 9:49. 09, 10:54. 54, and 12:00. (0. 45 minutes are exactly 27. 27 seconds.) See also [ ] • References [ ]

Enter Time or Angle in Degrees Calculate the angle between the hands of the clock if the time is 8: 40 H = 8 M = 40 Calculate ∠ between 12 and 8There are 360° in a full circle (clock) There are 12 hours Each hour = 360/12 = 30° Hour FormulaHours = 30( H) Hours = 30( 8) θh = 240 Minute FormulaEach minute is 1/60 of an hour. Each hour represents 30 degrees. Minutes Angle = M(30)/60 → M/2: θm= M 2 θm= 40 2 θm = 20 Calculate ∠ between the clock: ΔθΔθ = |θh + θm| Δθ = |240 + 20| Δθ = |260| Hands in opposite direction:Clockwise + counter-clockwise = 360° Subtract our clockwise angle from 360° Angle 2 = 360 - 260°

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12 Thermodynamics • Introduction • 12.1 Zeroth Law of Thermodynamics: Thermal Equilibrium • 12.2 First law of Thermodynamics: Thermal Energy and Work • 12.3 Second Law of Thermodynamics: Entropy • 12.4 Applications of Thermodynamics: Heat Engines, Heat Pumps, and Refrigerators • Key Terms • Section Summary • Key Equations • 22 The Atom • Introduction • 22.1 The Structure of the Atom • 22.2 Nuclear Forces and Radioactivity • 22.3 Half Life and Radiometric Dating • 22.4 Nuclear Fission and Fusion • 22.5 Medical Applications of Radioactivity: Diagnostic Imaging and Radiation • Key Terms • Section Summary • Key Equations • Teacher Support The learning objectives in this section will help your students master the following standards: • (4) Science concepts. The student knows and applies the laws governing motion in a variety of situations. The student is expected to: • (C) analyze and describe accelerated motion in two dimensions using equations, including projectile and circular examples. Section Key Terms angle of rotation angular velocity arc length circular motion radius of curvature rotational motion spin tangential velocity Angle of Rotation What exactly do we mean by circular motion or rotation? Rotational motion is the circular motion of an object about an axis of rotation. We will discuss specifically circular motion and spin. Circular motion is when an object moves in a circular path. Examples of circular motion include a race car speeding around a circular curve, a t...

Enter Time or Angle in Degrees Calculate the angle between the hands of the clock if the time is 8: 40 H = 8 M = 40 Calculate ∠ between 12 and 8There are 360° in a full circle (clock) There are 12 hours Each hour = 360/12 = 30° Hour FormulaHours = 30( H) Hours = 30( 8) θh = 240 Minute FormulaEach minute is 1/60 of an hour. Each hour represents 30 degrees. Minutes Angle = M(30)/60 → M/2: θm= M 2 θm= 40 2 θm = 20 Calculate ∠ between the clock: ΔθΔθ = |θh + θm| Δθ = |240 + 20| Δθ = |260| Hands in opposite direction:Clockwise + counter-clockwise = 360° Subtract our clockwise angle from 360° Angle 2 = 360 - 260°

Activity: Clocks and Angles This activity is about What is the angle between the hands of a clock at 1 o'clock? At 1 o'clock the minute hand (red) points to the 12 and the hour hand (blue) points to the 1. So we need to find the angle between the 12 and the 1. How many of this angle are there in a complete turn? There are 12 of them in a complete turn (360°), so each one must be 360°÷ 12 = 30° So the angle between the hands of a clock at 1 o'clock is 30° . Note: • It doesn't matter whether we are talking about 1 am or 1 pm, the answer is exactly the same for both. • The angle between the hands at 1 o'clock could also be given as the reflex angle 330°, but we will always give the smaller (acute or obtuse) angle. What is the angle between the hands of a clock at 2:30? At 2:30 the minute hand (red) points to the 6 and the hour hand (blue) points halfway between the 2 and the 3. So how many lots of 30° do we have this time? • The angle between the 5 and the 6 is 30° • The angle between the 4 and the 5 is 30° • The angle between the 3 and the 4 is 30° • The remaining angle is ½× 30° = 15° So the angle between the hands of a clock at 2:30 = 30° + 30° + 30° + 15° = 105° Your Turn Complete the following table (give the smaller angle in each case): Time 1:00 2:30 7:00 10:30 11:20 3:40 5:15 8:45 Angle 30° 105° Check your answers at the bottom of the page. More Complicated Times Finding the angle between the hands of a clock is easy as long as we don't use complicated times. For exam...