radian and degree measure
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Angle- formed by rotating a ray about its endpoint (vertex)
Initial Side Starting position
Terminal Side Ending position
Standard Position
Initial side on positive x-axis and the vertex is on the origin
Angle describes the amount and direction of rotation120° –210°
Positive Angle- rotates counter-clockwise (CCW)
Negative Angle- rotates clockwise (CW)
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6.1 Radian and Degree Measure
Measuring Angles
The measure of an angle is determined by the amount of
rotation from the initial side to the terminal side.
There are two common ways to measure angles, in degrees
and in radians.
We’ll start with degrees, denoted by the symbol º.
One degree (1º) is equivalent to a rotation of of one
revolution.
1
360
Degrees, Minutes and Seconds
One complete revolution = 360± One minute:
One-sixtieth of a degree One minute is denoted 10
1O = 60
One second: One-sixtieth of a minute One second is denoted 100
10 = 6000
8
Angles are often classified according to the quadrant
in which their terminal sides lie.
Ex1: Name the quadrant in which each angle lies.
50º
208º II I
-75º III IV
6.1 Radian and Degree Measure
Classifying Angles
Quadrant 1
Quadrant 3
Quadrant 4
Basic Terminology
Quadrantal angle: Angle in standard position that doesn’t lie in any quadrant
Lies in quadrant II
Lies in quadrant IV
Quadrantal angle
10
6.1 Radian and Degree Measure
Coterminal Angles
Angles that have the same initial and terminal sides are
coterminal.
Angles and are coterminal.
Coterminal Angles: Two angles with the same initial and terminal sides
Find a positive coterminal angle to 20º
38036020
34036020Find a negative coterminal angle to 20
Radians
Central angle: An angle whose vertex is at the center of a circle Central angles subtend an arc on the circle
Definition of a Radian
A radian is the angle subtended at the centre of a circle by an arc whose length is equal to the radius of a circle.
RadiansAngle subtended at the centre by an arc of
length 1unit in a unit circle is said to have a measure of 1 radian.
The Radian
1 radian ≈ 57.3o 2 radians ≈ 114.6o 3 radians ≈ 171.9o
4 radians ≈ 229.2o 5 radians ≈ 286.5o 6 radians ≈ 343.8o
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