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Download 4.1 Radian and Degree Measure Trigonometry: "measurement of
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4.1 Radian and Degree Measure Trigonometry: "measurement of triangles" Angle: determined by rotating a ray about its endpoint Initial Side: starting position of the ray Terminal Side: position after rotation Vertex: endpoint of the ray Standard Position: the origin is the vertex and the initial side coincides with the positive xaxis Positive Angle: counterclockwise rotation Negative Angle: clockwise rotation Coterminal: angles with the same initial and terminal sides Measure of an Angle: the amount of rotation from the initial side to the terminal side Radian: http://en.wikipedia.org/wiki/Radian#mediaviewer/File:Circle_radians.gif http://upload.wikimedia.org/wikipedia/commons/4/4e/Circle_radians.gif Radian: One radian is the measure of a central angle that intercepts an arc s equal in length to the radius r of the circle. Because one full revolution is Acute Angles: Between: Obtuse Angles: Between: Determine the quadrant in which each angle lies. Angles are given in radians. Sketching and Finding Coterminal Angles Find a positive and negative coterminal angle for each given angle. Complementary Angles: Two angles that sum to Supplementary Angles: Two angles that sum to If possible, find the complement and supplement of: Conversions Between Degrees and Radians To Convert Degrees to Radians: Multiply By: To Convert Radians to Degrees: Multiply By: Convert From Degrees to Radians: To Convert Degrees to Radians: Multiply By: Convert From Radians to Degrees: To Convert Radians to Degrees: Multiply By: Applications Arc Length Arc Length A circle has a radius of 4 inches. Find the length of the arc intercepted by a central angle of Applications Linear and Angular Speed Linear Speed = Angular Speed = how fast the particle moves how fast the angle changes A lawn roller with a 10inch radius makes 1.2 revolutions per second. a.) Find the angular speed of the roller in radians per second. b.) Find the speed of the tractor that is pulling the roller.
