Vocabulary
Initial and Terminal Side of an Angle- In a coordinate plane an angle can be formed by fixing one ray, called the initial side and rotating the other, ray called the terminal side about the vertex.
Standard Position of an Angle- In a coordinate plane, the position of an angle whose vertex is at the origin and whose initial side lies on the positive x-axis.
Coterminal Angles- Angles in standard position with terminal sides that coincide.
Radian- In a circle with radius r and center at the origin, one radian is the measure of an angle in standard position whose terminal side intercepts an arc length r.
Sector- A region of a circle that is bounded by two radii and an arc of the circle. The central angle θ of a sector is the angle formed by the two radii.
Central Angle- An angle formed by two radii of a circle.
Standard Position of an Angle- In a coordinate plane, the position of an angle whose vertex is at the origin and whose initial side lies on the positive x-axis.
Coterminal Angles- Angles in standard position with terminal sides that coincide.
Radian- In a circle with radius r and center at the origin, one radian is the measure of an angle in standard position whose terminal side intercepts an arc length r.
Sector- A region of a circle that is bounded by two radii and an arc of the circle. The central angle θ of a sector is the angle formed by the two radii.
Central Angle- An angle formed by two radii of a circle.
Essential Information
Angles is Standard Position
In a coordinate plane, an angle can be formed by fixing one ray, called the initial side, and rotating the other ray, called the terminal side, about the vertex. An angle is in standard position if its vertex is at the origin and its initial side lies on the positive x-axis. |
The measure of an angle is positive if the rotation of its terminal side is counterclockwise, and negative if the rotation is clockwise. The terminal aide of an angle can move more than one complete rotation.
Coterminal Angles
Angles are coterminal if their terminal sides coincide. An angle coterminal with a given angle can be found by adding or subtracting multiples of 360⁰.
Angles are coterminal if their terminal sides coincide. An angle coterminal with a given angle can be found by adding or subtracting multiples of 360⁰.
Radian Measure
Angles can also be measured in radians. To define a radian, consider a circle with radius r centered at the origin. One radian is the measure of an angle in standard position whose terminal side intercepts an arc of length r. Because the circumference of a circle is 2πr, there are 2π radians in a full circle. Degree measure and radian measure are therefore related by the equation 360⁰ = 2π radians, or 180 = π radians. |
Converting Between Degrees to Radians
Sectors of Circles
A sector is a region of a circle that is bounded by two radii and an arc of the circle. The central angle θ of a sector is the angle formed by the two radii. There are simple formulas for the arc length and area of a sector when the central angle is measured in radians.
A sector is a region of a circle that is bounded by two radii and an arc of the circle. The central angle θ of a sector is the angle formed by the two radii. There are simple formulas for the arc length and area of a sector when the central angle is measured in radians.