Section+4.1+Angle+Measure

Section 4.1 Angle Measure - An angle is formed when two rays share the same endpoint. The common endpoint is called the vertex. Definition: Degree Measure of Angles - An angle formed by one complete counterclockwise rotation has measure 360 degrees, denoted 360 degrees. Definition: Radian Measure - If a centeral angle theta in a circle with radius r intercepts an arc on the circle of length s, then the measure of theta, in radians, is given by Theta(in radians) = s/r Note: The formula is valid if and only if s (arc length) and r (radius) are expressed in the same units. Definition: Standard Position - An angle is said to be in standard position if its initial side is along the positive x-axis and its vertex is at the origin. Definition:Coterminal Angles - Two angles in standard position with the same terminal side are called cotermininal angles. Definition: Arc Length - If a central angle theta in a circle with radius r intercepts an arc on the circle of length s, then the arc length is given by... s = r(theta) theta is given in radians Definition: Area of a Circular Sector - The area of a sector of a circle with radius r and central angle theta is given by A=1/2r^2(theta) theta is given in radians Definition: Linear Speed - If a point P moves along the circumference of a circle at a constant speed, then the linear speed v is given by v= s/t where s is the arc length and t is the time. Definition: Angular Speed - If a point P moves along the circumference of a circle at a constant speed, then the centeral angle (theta) that is formed with the terminal side passing through point P also changes over some time t at a constant speed. The angular speed w (omega) is given by.... w = theta / t - If a point P moves at a constant speed along the circumference of a circle with radius r, then the linear speed v and the angular speed w are related by v = rw or w = v / r Note: This relationship is true only when theta is given in radians.
 * Degrees and Radians**
 * Coterminal Angles: Angles in Standard Position**
 * Coterminal Angles:**
 * Arc Length**
 * Area of a Circular Sector**
 * Relating Linear and Angular Speeds**