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Unformatted text preview: PreCalculus 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 xaxis. 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 xaxis or yaxis * An acute angle is one which measures 90 < < θ or 2 π θ < < radians. A right angle is one which measures 90 = θ or 2 π θ = radians or ( 4 1 rotation). An obtuse angle is one which measures 180 90 < < θ or π θ π < < 2 radians. A straight angle is one which measures 180 = θ or π θ = 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, θ , that intercepts the arc is r s = θ radians. * To convert from degrees to radians, multiply the # of degrees by 180 π . To convert from radians to degrees, multiply the # of radians by π 180 . * 360 = π 2 radians = 1 revolution. * Let r be the radius of a circle and θ the nonnegative radian measure of a central angle of the circle. Then, the length of the arc intercepted by the central angle is θ r s = . If a point is motion on a circle of radius r through an angle of θ radians in time t, then the linear speed is t s v = where s is the arc length given by θ r s = , and its angular speed is t w θ = . 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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 Fall '08
 Mcbride,V
 Calculus, PreCalculus, Trigonometry, Cos

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