Radian and Degree Measure
|Topic Review on "Title":
An angle consists of two rays, R1 and R2, with a common vertex.
Standard position of an angle:
An angle is said to be in standard position if its vertex is at the origin of a rectangular coordinate system and its initial side coincides with the positive x-axis.
Two angles in standard position are said to be co-terminal if they have the same initial and terminal sides.
For a circle of radius , a central angle of radius subtends and arc whose length is
is measured in radians.
Area of a sector:
The area of the sector of a circle of radius formed by a central angle radians is
where the unit of angle must be in radians.
Linear speed: The linear speed is defined as .
Angular speed: The angular speed is defined as .
|Rapid Study Kit for "Title":
|Core Concept Tutorial
||Problem Solving Drill
||Review Cheat Sheet
|"Title" Tutorial Summary :
This tutorial mentions radians and degrees. The geometric definition of angles is shown with the use of examples. The standard position of an angle is shown with the development of graphs and angle relations.
Angle Measure is discussed along with radian measure because of their need in application problems such as circular motion related ones. Angular velocity and area of sector principles are motivated thanks in part to the idea of converting degree measure to radian measure.
Specific Tutorial Features:
• Problem-solving techniques are used to work out and illustrate the example problems, step by step.
• Converting degrees to radians are shown in the examples.
• Concept map showing inter-connections of new concepts in this tutorial and those previously introduced.
• Definition slides introduce terms as they are needed.
• Visual representation of concepts
• Animated examples—worked out step by step
• A concise summary is given at the conclusion of the tutorial.
|"Title" Topic List:
Arc Length and Examples
Relation between Degrees and Radians
Linear Speed and Angular Speed
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