The minute hand of a clock is 6 inches long and moves from 12 to 4 o'clock. how far does the tip of the minute hand move? express your answer in terms of pi and then round to 2 decimal places.

12.56 inches

Step-by-step explanation: First, when know the following:

A clock is a circle, so the total movement, from 12 to 12 is 360° or 2π.

It is also know that a circle circunference (The total size of the circle on a straight line) is 2π * Radius

The minute hand does a circle on its travel, that circle radius is equal to 6 inches.

The movement from 12 to 4 is a third (4/12 = 1/3). Knowing this:

120° = (1/3) * 360° = (1/3) * 2π = (2/3) * π

So the travel from 12 to 4 is (2/3)π

To know the distance on inches, we multiply the distance on radians per the radius.

Total distance = 6 * (2/3)π

Total distance = 4π inches

Total distance = 12.56 inches

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step-by-step explanation:

sin(7pi/6 - pi/3)  

= sin(7pi/6 - 2pi/6)  

= sin(5pi/6)  

= sin(pi - pi/6)  

= sin(pi/6)  

= 1/2  

sin 7pi/6 - sin pi/3  

= sin (pi + pi/6) - sin pi/3  

= -sin pi/6 - sin pi/3  

= -1/2 - sqrt(3)/2  

= -(1+sqrt(3))2