Download 4.1 Radian and Degree Measure Trigonometry: "measurement of

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.