5.1 Angles  (Page 9/29)

Key equations

Key concepts

• An angle is formed from the union of two rays, by keeping the initial side fixed and rotating the terminal side. The amount of rotation determines the measure of the angle.
• An angle is in standard position if its vertex is at the origin and its initial side lies along the positive x -axis. A positive angle is measured counterclockwise from the initial side and a negative angle is measured clockwise.
• To draw an angle in standard position, draw the initial side along the positive x -axis and then place the terminal side according to the fraction of a full rotation the angle represents. See [link] .
• In addition to degrees, the measure of an angle can be described in radians. See [link] .
• To convert between degrees and radians, use the proportion $\frac{\theta }{180}=\frac{{\theta }^R}{\pi }.$ See [link] and [link] .
• Two angles that have the same terminal side are called coterminal angles.
• We can find coterminal angles by adding or subtracting 360° or $2\pi .$ See [link] and [link] .
• Coterminal angles can be found using radians just as they are for degrees. See [link] .
• The length of a circular arc is a fraction of the circumference of the entire circle. See [link] .
• The area of sector is a fraction of the area of the entire circle. See [link] .
• An object moving in a circular path has both linear and angular speed.
• The angular speed of an object traveling in a circular path is the measure of the angle through which it turns in a unit of time. See [link] .
• The linear speed of an object traveling along a circular path is the distance it travels in a unit of time. See [link] .

Section exercises

Verbal

Draw an angle in standard position. Label the vertex, initial side, and terminal side.

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