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Unformatted text preview: Pre-Calculus Exam 4 (Section 4.1 4.8) Review Section 4.1 * An angle is in standard position if its vertex is at the origin of the rectangular coordinate system and its initial side lies above the positive x-axis. A positive angle is generated by counterclockwise rotation. A negative angle is generated by clockwise rotation. *A quadrantal angle is an angle with its terminal side on the x-axis or y-axis * An acute angle is one which measures 90 < < or 2 < < radians. A right angle is one which measures 90 = or 2 = radians or ( 4 1 rotation). An obtuse angle is one which measures 180 90 < < or < < 2 radians. A straight angle is one which measures 180 = or = radians or ( 2 1 rotation). * Two angles with the same initial and terminal sides are called coterminal angles (An angle of x is coterminal with angles of 360 + k x , where k is an interger). * One radian is the measure of the central angle of a circle that intercepts an arc equal in length to the radius of the circle. Consider an arc of length s on a circle of radius r. The measure of the central angle, , that intercepts the arc is r s = radians. * To convert from degrees to radians, multiply the # of degrees by 180 . To convert from radians to degrees, multiply the # of radians by 180 . * 360 = 2 radians = 1 revolution. * Let r be the radius of a circle and the nonnegative radian measure of a central angle of the circle. Then, the length of the arc intercepted by the central angle is r s = . If a point is motion on a circle of radius r through an angle of radians in time t, then the linear speed is t s v = where s is the arc length given by r s = , and its angular speed is t w = . The linear speed, v, of a point a distance r from the center of rotation is given by rw v = where w is the angular speed in radians per unit of time....
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