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Angles and their measure
Transcript of Angles and their measure
An angle is determined by rotating a ray (half-line) about its endpoint. The starting position of the ray is the INITIAL SIDE of the angle, and the position after rotation is the TERMINAL SIDE
Two angles are coterminals if they are drawn in the standrard position and they have their terminal sides in the same location.
The measure of an angle is determined by the amount of rotation from the initial side to the terminal side. The most common unit of an angle measure is the degree (º).
Right angle: quarter revolution (90º)
Straight angle: half revolution (180º)
Full revolution (360º)
when the vertex is at the origin and the initial side coincides with the positive x-axis
Positive and Negative Angles
Such an angle is in standard position, POSITIVE angles are generated by counterclockwise rotation, and NEGATIVE angles by clockwise rotaion.
angles between 0º and 90º
angles between 90º and 180º
one radian is the masure of a central angle Ө that intercepts an arc s equal in length to the radius r of the circle,
Conversions Between Degrees and Radians
to convert degrees to radians, multiply degrees by π/180
to convert radiands to degrees, multiply radians by 180/ π
for a circle of radius r, a central angle Ө an arc length s given by : s=rӨ
where Ө is measured in radians
Linear and Angular Speed
Linear speed ν=arc length /time =s/t
Angular speed ω=central angle/ time =Ө/t
Area of a Sector of a Circle
For a circle of radius r, the area A of a sector of the circle with central angle Ө is given by:
A=(1/2) r^2 θ