Sam Albee Radians and radians
Radians and radians
The radian as a unit for measuring angles is obtained in this way:
In any sector of a circle, the length of the arc b is proportional to the central angle (midpoint angle) α of the sector of the circle and to the radius r of the circle - do my homework . If b is the length of the arc and α the size of the associated central angle, then, starting from the circumference of the circle b/(2π⋅r)=α/360° or transformed b/r=(α⋅π)/180°.
If one chooses the radius 1 (i.e. the unit circle), the length of the arc b can be given for each angle α - algebra homework help . The radian b of an angle α is the measure of the length of the corresponding arc on the unit circle:
b=(α⋅π⋅r)/180°.
The unit in radians is the radian (1 rad).
1 rad is the angle for which the arc on the unit circle has length 1. It is:
1 rad = 57° 17'45''
1°=π/180rad = 0.017453 rad
When specifying angular quantities in radians, the unit rad is usually omitted:
360°=2π 180°=π 90°=π/2 60°=π/3
The difference between an angle and its size is not expressed here by different symbols because it is clear from the context whether an angle or its size is meant.
The notation α = 60º means that the angle α has a size of 6 0 degrees.
Specifying the size of oriented angles
When stating the size of oriented angles - math homework help , it is necessary to also state the orientation of the angle.
The angles ∢ (p, q) and ∢ (q, p) are equal in magnitude but oriented in opposite directions. Counterclockwise rotations correspond to positive orientation. The corresponding angular measure has a positive sign. Clockwise rotations correspond to the negative orientation. The corresponding angular measure has a negative sign.
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