In this lesson we will learn to: describe angles, use radian measure, use degree measure, use angles to model and solve real-world problems.
J. Robert Buchanan
Radian and Degree Measure
Background We now begin a study of trigonometry (Greek for “measurement of triangles”).
Terminal Side
Vertex
Initial Side
J. Robert Buchanan
Radian and Degree Measure
Standard Position If the vertex is the origin and the initial side lies along the positive x-axis, the angle is said to be in standard position. y
Terminal Side
x
Initial Side
J. Robert Buchanan
Radian and Degree Measure
Orientation and Notation
Angles will be named by uppercase letters (A, B, C, . . . ) or Greek letters (α, β, γ, . . . ). An angle is positive if it is generated by rotating the terminal side counterclockwise (abbreviated ccw) from the initial side. An angle is negative if it is generated by rotating the terminal side clockwise (abbreviated cw) from the initial side. Angles that have the same initial and terminal sides are called coterminal angles.
J. Robert Buchanan
Radian and Degree Measure
Radian Measure
Definition One radian is the measure of a central angle θ that intercepts an arc s equal in length to the radius r of the circle. If θ is the radian measure of the angle then θ=
s . r
Recall: the circumference of a circle is C = 2πr , thus the radian measure of one complete revolution is θ=
