#### Transcript of Angles and their measure

**Angles and their measure**

**Angles**

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

Coterminal Angles

Two angles are coterminals if they are drawn in the standrard position and they have their terminal sides in the same location.

Degree Measure

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).

more angles...

Right angle: quarter revolution (90º)

Straight angle: half revolution (180º)

Full revolution (360º)

Standard Position

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.

Acute angles

angles between 0º and 90º

Obtuse angles

angles between 90º and 180º

Radian Measure

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,

Ө=s/r

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

Arc Length

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

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