Turn an angle past 360 degrees, or backwards, and measure it in radians, the natural unit of a circle. Then use radians to find arcs and sectors of wheels, clocks and tracks.
3 lessons, about 1 h 25 min3 simulations11 problems6 practice questionsPython in every lesson
Created by StemPy LabAn angle is the amount of turning from an initial side to a terminal side. Anticlockwise turns are positive and clockwise turns are negative, and a turn can go past one revolution. Angles that differ by a multiple of end in the same place. A degree splits into minutes, and a minute into seconds.
A radian is the angle at the centre of a circle that cuts off an arc as long as the radius. In general the angle in radians is the arc divided by the radius. A full turn is radians, so radians is . Multiply by to change degrees into radians, and by to change back.
With the angle in radians, an arc of a circle is and a sector has the area . A wheel that rolls moves forward one circumference in each turn. The angular speed is the angle turned each second, and a point on the rim moves at .
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